Review

Criteria

Reviews are a feature of the journal that may include, but are not limited to, the following types of articles:

systematic and substantial syntheses of specific research areas,
evaluations of progress in specified areas,
critical assessments with respect to issues

within the scope of Fixed Point Theory and Algorithms for Sciences and Engineering.

Preparing your manuscript

Title page

The title page should:

present a title that includes, if appropriate, the research design or for non-research studies: a description of what the article reports
list the full names and institutional addresses for all authors
- if a collaboration group should be listed as an author, please list the group name as an author and include the names of the individual members of the group in the “Acknowledgements” section in accordance with the instructions below
- Large Language Models (LLMs), such as ChatGPT, do not currently satisfy our authorship criteria. Notably an attribution of authorship carries with it accountability for the work, which cannot be effectively applied to LLMs. Use of an LLM should be properly documented in the Methods section (and if a Methods section is not available, in a suitable alternative part) of the manuscript
indicate the corresponding author

Abstract

The abstract should briefly summarize the aim, findings or purpose of the article. Please minimize the use of abbreviations and do not cite references in the abstract.

Keywords

Three to ten keywords representing the main content of the article.

Main text

This should contain the body of the article, and may also be broken into subsections with short, informative headings.

List of abbreviations

If abbreviations are used in the text they should be defined in the text at first use, and a list of abbreviations should be provided.

Declarations

All manuscripts must contain the following sections under the heading 'Declarations':

Availability of data and materials
Competing interests
Funding
Authors' contributions
Acknowledgements
Authors' information (optional)

Please see below for details on the information to be included in these sections.

If any of the sections are not relevant to your manuscript, please include the heading and write 'Not applicable' for that section.

Availability of data and materials

All manuscripts must include an ‘Availability of data and materials’ statement. Data availability statements should include information on where data supporting the results reported in the article can be found including, where applicable, hyperlinks to publicly archived datasets analysed or generated during the study. By data we mean the minimal dataset that would be necessary to interpret, replicate and build upon the findings reported in the article. We recognise it is not always possible to share research data publicly, for instance when individual privacy could be compromised, and in such instances data availability should still be stated in the manuscript along with any conditions for access.

Data availability statements can take one of the following forms (or a combination of more than one if required for multiple datasets):

The datasets generated and/or analysed during the current study are available in the [NAME] repository, [PERSISTENT WEB LINK TO DATASETS]
The datasets used and/or analysed during the current study are available from the corresponding author on reasonable request.
All data generated or analysed during this study are included in this published article [and its supplementary information files].
The datasets generated and/or analysed during the current study are not publicly available due [REASON WHY DATA ARE NOT PUBLIC] but are available from the corresponding author on reasonable request.
Data sharing is not applicable to this article as no datasets were generated or analysed during the current study.
The data that support the findings of this study are available from [third party name] but restrictions apply to the availability of these data, which were used under license for the current study, and so are not publicly available. Data are however available from the authors upon reasonable request and with permission of [third party name].
Not applicable. If your manuscript does not contain any data, please state 'Not applicable' in this section.

More examples of template data availability statements, which include examples of openly available and restricted access datasets, are available here.

SpringerOpen also requires that authors cite any publicly available data on which the conclusions of the paper rely in the manuscript. Data citations should include a persistent identifier (such as a DOI) and should ideally be included in the reference list. Citations of datasets, when they appear in the reference list, should include the minimum information recommended by DataCite and follow journal style. Dataset identifiers including DOIs should be expressed as full URLs. For example:

Hao Z, AghaKouchak A, Nakhjiri N, Farahmand A. Global integrated drought monitoring and prediction system (GIDMaPS) data sets. figshare. 2014. http://dx.doi.org/10.6084/m9.figshare.853801

With the corresponding text in the Availability of data and materials statement:

The datasets generated during and/or analysed during the current study are available in the [NAME] repository, [PERSISTENT WEB LINK TO DATASETS].^{[Reference number]}

If you wish to co-submit a data note describing your data to be published in BMC Research Notes, you can do so by visiting our submission portal. Data notes support open data and help authors to comply with funder policies on data sharing. Co-published data notes will be linked to the research article the data support (example).

Competing interests

All financial and non-financial competing interests must be declared in this section.

See our editorial policies for a full explanation of competing interests. If you are unsure whether you or any of your co-authors have a competing interest please contact the editorial office.

Please use the authors’ initials to refer to each authors' competing interests in this section.

If you do not have any competing interests, please state "The authors declare that they have no competing interests" in this section.

Funding

All sources of funding for the research reported should be declared. If the funder has a specific role in the conceptualization, design, data collection, analysis, decision to publish, or preparation of the manuscript, this should be declared.

Authors' contributions

The individual contributions of authors to the manuscript should be specified in this section. Guidance and criteria for authorship can be found in our editorial policies.

Please use initials to refer to each author's contribution in this section, for example: "FC analyzed and interpreted the patient data regarding the hematological disease and the transplant. RH performed the histological examination of the kidney, and was a major contributor in writing the manuscript. All authors read and approved the final manuscript."

Acknowledgements

Please acknowledge anyone who contributed towards the article who does not meet the criteria for authorship including anyone who provided professional writing services or materials.

Authors should obtain permission to acknowledge from all those mentioned in the Acknowledgements section.

See our editorial policies for a full explanation of acknowledgements and authorship criteria.

If you do not have anyone to acknowledge, please write "Not applicable" in this section.

Group authorship (for manuscripts involving a collaboration group): if you would like the names of the individual members of a collaboration Group to be searchable through their individual PubMed records, please ensure that the title of the collaboration Group is included on the title page and in the submission system and also include collaborating author names as the last paragraph of the “Acknowledgements” section. Please add authors in the format First Name, Middle initial(s) (optional), Last Name. You can add institution or country information for each author if you wish, but this should be consistent across all authors.

Authors' information

This section is optional.

You may choose to use this section to include any relevant information about the author(s) that may aid the reader's interpretation of the article, and understand the standpoint of the author(s). This may include details about the authors' qualifications, current positions they hold at institutions or societies, or any other relevant background information. Please refer to authors using their initials. Note this section should not be used to describe any competing interests.

Footnotes

Footnotes should be designated within the text using a superscript number. It is not allowed to use footnotes for references/citations.

How to format your references

Examples of the Math and Physical Sciences reference style are shown below. Please ensure that the reference style is followed precisely; if the references are not in the correct style, they may need to be retyped and carefully proofread.

Web links and URLs: All web links and URLs, including links to the authors' own websites, should be given a reference number and included in the reference list rather than within the text of the manuscript. They should be provided in full, including both the title of the site and the URL, as well as the date the site was accessed, in the following format: The Mouse Tumor Biology Database. http://tumor.informatics.jax.org/mtbwi/index.do. Accessed 20 May 2013. If an author or group of authors can clearly be associated with a web link, such as for weblogs, then they should be included in the reference.

Authors may wish to make use of reference management software to ensure that reference lists are correctly formatted. An example of such software is Papers, which is part of Springer Science+Business Media.

Example reference style:

Article within a journal

Hamburger, C: Quasimonotonicity, regularity and duality for nonlinear systems of partial differential equations. Ann. Mat. Pura. Appl. 169, 321-354 (1995).

Article by DOI (with page numbers)

Slifka, MK, Whitton, JL: Clinical implications of dysregulated cytokine production. J. Mol. Med. 78, 74-80 (2000). doi:10.1007/s001090000086.

Article by DOI (before issue publication and with page numbers)

Slifka, MK, Whitton, JL: Clinical implications of dysregulated cytokine production. J. Mol. Med. (2000). doi:10.1007/s001090000086.

Article in electronic journal by DOI (no paginated version)

Slifka, MK, Whitton, JL: Clinical implications of dysregulated cytokine production. Dig. J. Mol. Med. (2000). doi:10.1007/s801090000086.

Journal issue with issue editor

Smith, J (ed.): Rodent genes. Mod. Genomics J. 14(6), 126-233 (1998).

Journal issue with no issue editor

Rodent genes: Mod. Genomics J. 14(6):126-233 (1998).

Book chapter, or an article within a book

Broy, M: Software engineering - from auxiliary to key technologies. In: Broy, M, Denert, E (eds.) Software Pioneers, pp. 10-13. Springer, New York (2002).

Complete book, authored

Geddes, KO, Czapor, SR, Labahn, G: Algorithms for Computer Algebra. Kluwer, Boston (1992).

Complete book, edited

Seymour, RS (ed.): Conductive Polymers. Plenum, New York (1981).

Chapter in a book in a series without volume titles

MacKay, DM: Visual stability and voluntary eye movements. In: Jung, R, MacKay, DM (eds.) Handbook of Sensory Physiology, vol. 3, pp. 307-331. Springer, Heidelberg (1973).

Chapter in a book in a series with volume titles

Smith, SE: Neuromuscular blocking drugs in man. In: Zaimis, E (ed.) Neuromuscular Junction. Handbook of Experimental Pharmacology, vol. 42, pp. 593-660. Springer, Heidelberg (1976).

OnlineFirst chapter in a series (without a volume designation but with a DOI)

Saito, Y, Hyuga, H. Rate equation approaches to amplification of enantiomeric excess and chiral symmetry breaking. Top. Curr. Chem. (2007). doi:10.1007/128_2006_108.

Proceedings as a book (in a series and subseries)

Zowghi, D: A framework for reasoning about requirements in evolution. In: Foo N., Goebel R. (eds.) Topics in Artificial Intelligence, 4th Pacific Rim Conference on Artificial Intelligence, Cairns, August 1996. Lecture Notes in Computer Science. Lecture Notes in Artificial Intelligence, vol. 1114, pp. 157-168. Springer, Heidelberg (1996).

Article within conference proceedings with an editor (without a publisher)

Aaron, M: The future of genomics. In: Williams, H (ed.) Proceedings of the Genomic Researchers, Boston (1999).

Article within conference proceedings without an editor (without a publisher)

Chung, S-T, Morris, RL: Isolation and characterization of plasmid deoxyribonucleic acid from Streptomyces fradiae. In: Abstracts of the 3rd International Symposium on the Genetics of Industrial Microorganisms, University of Wisconsin, Madison, 4-9 June 1978.

Article presented at a conference

Chung, S-T, Morris, RL: Isolation and characterization of plasmid deoxyribonucleic acid from Streptomyces fradiae. Paper presented at the 3rd international symposium on the genetics of industrial microorganisms, University of Wisconsin, Madison, 4-9 June 1978.

Patent

Norman, LO: Lightning rods. US Patent 4,379,752, 9 Sept 1998.

Dissertation, PhD thesis

Trent, JW: Experimental acute renal failure. Dissertation, University of California (1975).

Book with institutional author

International Anatomical Nomenclature Committee: Nomina anatomica. Excerpta Medica, Amsterdam (1966).

In press article

Holmes, R: References. In: Jones, TC (ed.) Science style manual. Sprint, London (2007, in press).

Online document

Cartwright, J: Big stars have weather too. IOP Publishing PhysicsWeb. http://physicsweb.org/articles/news/11/6/16/1 (2007). Accessed 26 June 2007.

Online database

Healthwise Knowledgebase. US Pharmacopeia, Rockville. http://www.healthwise.org (1998). Accessed 21 Sept 1998.

Supplementary material/private homepage

Doe, J: Title of supplementary material. http://www.privatehomepage.com (2000). Accessed 22 Feb 2000.

University site

Doe, J: Title of preprint. http://www.uni-heidelberg.de/mydata.html (1999). Accessed 25 Dec 1999.

FTP site

Doe, J: Trivial HTTP, RFC2169. ftp://ftp.isi.edu/in-notes/rfc2169.txt (1999). Accessed 12 Nov 1999.

Organization site

ISSN International Centre: The ISSN register. http://www.issn.org (2006). Accessed 20 Feb 2007.

General formatting information

Manuscripts must be written in concise English. For help on scientific writing, or preparing your manuscript in English, please see Springer's Author Academy.

Quick points:

Use double line spacing
Include line and page numbering
Use SI units: Please ensure that all special characters used are embedded in the text, otherwise they will be lost during conversion to PDF
Do not use page breaks in your manuscript

File formats

The following word processor file formats are acceptable for the main manuscript document:

Microsoft word (DOC, DOCX)
Rich text format (RTF)
TeX/LaTeX

Please note: editable files are required for processing in production. If your manuscript contains any non-editable files (such as PDFs) you will be required to re-submit an editable file if your manuscript is accepted.

For more information, see 'Preparing figures' below.

Additional information for TeX/LaTeX users

You are encouraged to use the Springer Nature LaTeX template when preparing a submission. A PDF of your manuscript files will be compiled during submission using pdfLaTeX and TexLive 2021.

All relevant editable source files must be uploaded during the submission process. Failing to submit these source files will cause unnecessary delays in the production process.

Style and language

For editors and reviewers to accurately assess the work presented in your manuscript you need to ensure the English language is of sufficient quality to be understood. If you need help with writing in English you should consider:

Getting a fast, free online grammar check.
Visiting the English language tutorial which covers the common mistakes when writing in English.
Asking a colleague who is proficient in English to review your manuscript for clarity.
Using a professional language editing service where editors will improve the English to ensure that your meaning is clear and identify problems that require your review. Two such services are provided by our affiliates Nature Research Editing Service and American Journal Experts. SpringerOpen authors are entitled to a 10% discount on their first submission to either of these services. To claim 10% off English editing from Nature Research Editing Service, click here. To claim 10% off American Journal Experts, click here.

Please note that the use of a language editing service is not a requirement for publication in Fixed Point Theory and Algorithms for Sciences and Engineering and does not imply or guarantee that the article will be selected for peer review or accepted.

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获取快速、免费的在线语法检查。
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请一位以英语为母语的同事审阅您的稿件是否表意清晰。
使用专业语言编辑服务，编辑人员会对英语进行润色，以确保您的意思表达清晰，并提出需要您复核的问题。例如我们的附属机构 Nature Research Editing Service 以及合作伙伴 American Journal Experts 都可以提供此类专业服务。SpringerOpen作者享受首次订单10%优惠，该优惠同时适用于两家公司。您只需点击以下链接即可开始。使用 Nature Research Editing Service的编辑润色10%的优惠服务，请点击这里。使用 American Journal Experts的10%优惠服务，请点击这里。

请注意，使用语言编辑服务并非在期刊上发表文章的必要条件，这也并不意味或保证文章将被选中进行同行评议或被接受。

エディターと査読者があなたの論文を正しく評価するには、使用されている英語の質が十分であることが必要とされます。英語での論文執筆に際してサポートが必要な場合には、次のオプションがあります：

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プロの英文校正サービスを利用する。校正者が原稿の意味を明確にしたり、問題点を指摘し、英語を向上させます。Nature Research Editing Service とAmerican Journal Experts の2つは弊社と提携しているサービスです。SpringerOpenのジャーナルの著者は、いずれかのサービスを初めて利用する際に、10%の割引を受けることができます。Nature Research Editing Serviceの10%割引を受けるには、こちらをクリックしてください。. American Journal Expertsの10%割引を受けるには、こちらをクリックしてください。

英文校正サービスの利用は、このジャーナルに掲載されるための条件ではないこと、また論文審査や受理を保証するものではないことに留意してください。

영어 원고의 경우, 에디터 및 리뷰어들이 귀하의 원고에 실린 결과물을 정확하게 평가할 수 있도록, 그들이 충분히 이해할 수 있을 만한 수준으로 작성되어야 합니다. 만약 영작문과 관련하여 도움을 받기를 원하신다면 다음의 사항들을 고려하여 주십시오:

영어 튜토리얼 페이지에 방문하여 영어로 글을 쓸 때 자주하는 실수들을 확인합니다.
귀하의 원고의 표현을 명확히 해줄 영어 원어민 동료를 찾아서 리뷰를 의뢰합니다
리뷰에 대비하여, 원고의 의미를 명확하게 해주고 리뷰에서 요구하는 문제점들을 식별해서 영문 수준을 향상시켜주는 전문 영문 교정 서비스를 이용합니다. Nature Research Editing Service와 American Journal Experts에서 저희와 협약을 통해 서비스를 제공하고 있습니다. SpringerOpen에서는 위의 두 가지의 서비스를 첫 논문 투고를 위해 사용하시는 경우, 10%의 할인을 제공하고 있습니다. Nature Research Editing Service이용시 10% 할인을 요청하기 위해서는 여기를 클릭해 주시고, American Journal Experts 이용시 10% 할인을 요청하기 위해서는 여기를 클릭해 주십시오.

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Data and materials

For all journals, SpringerOpen strongly encourages all datasets on which the conclusions of the manuscript rely to be either deposited in publicly available repositories (where available and appropriate) or presented in the main paper or additional supporting files, in machine-readable format (such as spread sheets rather than PDFs) whenever possible. Please see the list of recommended repositories in our editorial policies.

For some journals, deposition of the data on which the conclusions of the manuscript rely is an absolute requirement. Please check the Instructions for Authors for the relevant journal and article type for journal specific policies.

For all manuscripts, information about data availability should be detailed in an ‘Availability of data and materials’ section. For more information on the content of this section, please see the Declarations section of the relevant journal’s Instruction for Authors. For more information on SpringerOpen's policies on data availability, please see our editorial policies.

Formatting the 'Availability of data and materials' section of your manuscript

The following format for the 'Availability of data and materials section of your manuscript should be used:

"The dataset(s) supporting the conclusions of this article is(are) available in the [repository name] repository, [unique persistent identifier and hyperlink to dataset(s) in http:// format]."

The following format is required when data are included as additional files:

"The dataset(s) supporting the conclusions of this article is(are) included within the article (and its additional file(s))."

For databases, this section should state the web/ftp address at which the database is available and any restrictions to its use by non-academics.

For software, this section should include:

Project name: e.g. My bioinformatics project
Project home page: e.g. http://sourceforge.net/projects/mged
Archived version: DOI or unique identifier of archived software or code in repository (e.g. enodo)
Operating system(s): e.g. Platform independent
Programming language: e.g. Java
Other requirements: e.g. Java 1.3.1 or higher, Tomcat 4.0 or higher
License: e.g. GNU GPL, FreeBSD etc.
Any restrictions to use by non-academics: e.g. licence needed

Information on available repositories for other types of scientific data, including clinical data, can be found in our editorial policies.

References

See our editorial policies for author guidance on good citation practice.

What should be cited?

Only articles, clinical trial registration records and abstracts that have been published or are in press, or are available through public e-print/preprint servers, may be cited.

Unpublished abstracts, unpublished data and personal communications should not be included in the reference list, but may be included in the text and referred to as "unpublished observations" or "personal communications" giving the names of the involved researchers. Obtaining permission to quote personal communications and unpublished data from the cited colleagues is the responsibility of the author. Either footnotes or endnotes are permitted. Journal abbreviations follow Index Medicus/MEDLINE.

Any in press articles cited within the references and necessary for the reviewers' assessment of the manuscript should be made available if requested by the editorial office.

Preparing figures

When preparing figures, please follow the formatting instructions below.

Figure titles (max 15 words) and legends (max 300 words) should be provided in the main manuscript, not in the graphic file.
Tables should NOT be submitted as figures but should be included in the main manuscript file.
Multi-panel figures (those with parts a, b, c, d etc.) should be submitted as a single composite file that contains all parts of the figure.
Figures should be numbered in the order they are first mentioned in the text, and uploaded in this order.
Figures should be uploaded in the correct orientation.
Figure keys should be incorporated into the graphic, not into the legend of the figure.
Each figure should be closely cropped to minimize the amount of white space surrounding the illustration. Cropping figures improves accuracy when placing the figure in combination with other elements when the accepted manuscript is prepared for publication on our site. For more information on individual figure file formats, see our detailed instructions.
Individual figure files should not exceed 10 MB. If a suitable format is chosen, this file size is adequate for extremely high quality figures.
Please note that it is the responsibility of the author(s) to obtain permission from the copyright holder to reproduce figures (or tables) that have previously been published elsewhere. In order for all figures to be open access, authors must have permission from the rights holder if they wish to include images that have been published elsewhere in non open access journals. Permission should be indicated in the figure legend, and the original source included in the reference list.

Figure file types

We accept the following file formats for figures:

EPS (suitable for diagrams and/or images)
PDF (suitable for diagrams and/or images)
Microsoft Word (suitable for diagrams and/or images, figures must be a single page)
PowerPoint (suitable for diagrams and/or images, figures must be a single page)
TIFF (suitable for images)
JPEG (suitable for photographic images, less suitable for graphical images)
PNG (suitable for images)
BMP (suitable for images)
CDX (ChemDraw - suitable for molecular structures)

Figure size and resolution

Figures are resized during publication of the final full text and PDF versions to conform to the SpringerOpen standard dimensions, which are detailed below.

Figures on the web:

width of 600 pixels (standard), 1200 pixels (high resolution).

Figures in the final PDF version:

width of 85 mm for half page width figure
width of 170 mm for full page width figure
maximum height of 225 mm for figure and legend
image resolution of approximately 300 dpi (dots per inch) at the final size

Figures should be designed such that all information, including text, is legible at these dimensions. All lines should be wider than 0.25 pt when constrained to standard figure widths. All fonts must be embedded.

Figure file compression

Vector figures should if possible be submitted as PDF files, which are usually more compact than EPS files.

TIFF files should be saved with LZW compression, which is lossless (decreases file size without decreasing quality) in order to minimize upload time.
JPEG files should be saved at maximum quality.
Conversion of images between file types (especially lossy formats such as JPEG) should be kept to a minimum to avoid degradation of quality.

If you have any questions or are experiencing a problem with figures, please contact the customer service team at info@springeropen.com.

Preparing tables

When preparing tables, please follow the formatting instructions below.

Tables should be numbered and cited in the text in sequence using Arabic numerals (i.e. Table 1, Table 2 etc.).
Tables less than one A4 or Letter page in length can be placed in the appropriate location within the manuscript.
Tables larger than one A4 or Letter page in length can be placed at the end of the document text file. Please cite and indicate where the table should appear at the relevant location in the text file so that the table can be added in the correct place during production.
Larger datasets, or tables too wide for A4 or Letter landscape page can be uploaded as additional files. Please see [below] for more information.
Tabular data provided as additional files can be uploaded as an Excel spreadsheet (.xls ) or comma separated values (.csv). Please use the standard file extensions.
Table titles (max 15 words) should be included above the table, and legends (max 300 words) should be included underneath the table.
Tables should not be embedded as figures or spreadsheet files, but should be formatted using ‘Table object’ function in your word processing program.
Color and shading may not be used. Parts of the table can be highlighted using superscript, numbering, lettering, symbols or bold text, the meaning of which should be explained in a table legend.
Commas should not be used to indicate numerical values.

If you have any questions or are experiencing a problem with tables, please contact the customer service team at info@springeropen.com.

Preparing additional files

As the length and quantity of data is not restricted for many article types, authors can provide datasets, tables, movies, or other information as additional files.

All Additional files will be published along with the accepted article. Do not include files such as patient consent forms, certificates of language editing, or revised versions of the main manuscript document with tracked changes. Such files, if requested, should be sent by email to the journal’s editorial email address, quoting the manuscript reference number.

Results that would otherwise be indicated as "data not shown" should be included as additional files. Since many web links and URLs rapidly become broken, SpringerOpen requires that supporting data are included as additional files, or deposited in a recognized repository. Please do not link to data on a personal/departmental website. Do not include any individual participant details. The maximum file size for additional files is 20 MB each, and files will be virus-scanned on submission. Each additional file should be cited in sequence within the main body of text.

Submit manuscript