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We discuss the extension of some fundamental results in nonlinear analysis to the setting of gauge spaces. In particular, we establish Ekeland type and Caristi type results under suitable hypotheses for mappin...
In this paper, we give a fixed point theorem in locally convex algebras and present applications to the existence problem for a class of nonlinear integral equations with unbounded deviations.
Using the concept of a Boyd-Wong contraction, we obtain a simple, sufficient, and necessary condition for the convergence of the sequence of successive approximations to a unique fixed point.
In this paper, we construct an iterative process involving a hybrid pair of a finite family of generalized asymptotically nonexpansive single-valued mappings and a finite family of generalized nonexpansive mul...
In this paper, we define a new class of Reich type multi-valued contractions on a complete metric space satisfying the g-graph preserving condition and we study the fixed point theorem for such mappings. In addit...
We present new results regarding fixed point sets of various set-valued mappings using the concept of fixed point iteration schemes and the newly defined concept of fixed point resolutions. In particular, we p...
In this study, we introduce a three step iteration process and prove a convergence result for a countable family of pseudocontractive mappings. Our results improve and generalize most of the results that have ...
In this paper, we apply order-theoretic fixed point theorems and isotone selection theorems to study quasi-equilibrium problems. Some existence theorems of solutions to quasi-equilibrium problems are obtained ...
We discuss multivalued weakly Picard operators on partial Hausdorff metric spaces. First, we obtain Kikkawa-Suzuki type fixed point theorems for a new type of generalized contractive conditions. Then, we prove...
A new class of multivalued non-self-mappings, called SK-contractions with respect to b-generalized pseudodistances, is introduced and used to investigate the existence of best proximity points by using an appropr...
In this paper, we study the existence of fixed points of monotone nonexpansive mappings defined in Banach spaces endowed with a graph. This work is a continuity of the previous results of Ran and Reurings, Nieto
In this paper, the concept of ordered contractive mappings is introduced on cone metric spaces over Banach algebras, and some existence theorems of fixed points for such mappings are obtained. As an applicatio...
In this article, we first give an existence and uniqueness common best proximity points theorem for four mappings in a metric-type space
We give a generalization of the Banach contraction principle on a modular metric space endowed with a graph. The notion of a modular metric on an arbitrary set and the corresponding modular spaces, generalizin...
In this work, the concept of almost contraction for multi-valued mappings in the setting of cone metric spaces is defined and then we establish some fixed point and common fixed point results in the set-up of ...
In this work, we define the concept of G-monotone nonexpansive multivalued mappings defined on a metric space with a graph G. Then we obtain sufficient conditions for the existence of fixed points for such mappin...
In this paper, by using Minkowski functional introduced by Kadelburg et al. (Appl. Math. Lett. 24:370-374, 2011) or nonlinear scalarization function introduced by Du (Nonlinear Anal. 72:2259-2261, 2010), we prove...
The viscosity technique for the implicit midpoint rule of nonexpansive mappings in Hilbert spaces is established. The strong convergence of this technique is proved under certain assumptions imposed on the seq...
We introduce the new classes of Kannan-type maps with respect to u-distance and prove some fixed point theorems for these mappings. Then we present several examples to illustrate the main theorems.
In the paper, we introduce a new hybrid algorithm which is not based on the modification to weak convergence algorithms. The strong convergence theorem of the proposed algorithm is presented. Finally, the nume...
The aim of this paper is to introduce a class of multivalued mappings satisfying a Suzuki type generalized contractive condition in the framework of fuzzy metric spaces and to present fixed point results for s...
In this paper, a new modified Ishikawa iterative algorithm with errors by a shrinking projection method for generalized mixed equilibrium problems and a countable family of uniformly Bregman totally quasi-D-asymp...
The main aim of this paper is to study and establish some new coincidence point and common fixed point theorems for solutions of the stationary Schrödinger equation on cones. An interesting application is to i...
The Retraction Note to this article has been published in Fixed Point Theory and Applications 2020 2020:1
In this paper, inspired by two very different, successful metric theories such us the real view-point of Lowen’s approach spaces and the probabilistic field of Kramosil and Michálek’s fuzzy metric spaces, we pres...
In this work, we establish some fixed point theorems by revisiting the notion of ψ-contractive mapping in Menger PM-spaces. One of our results (namely, Theorem 2.3) may be viewed as a possible answer to the probl...
In this paper, we introduce a new algorithm for solving split equality mixed equilibrium problems in the framework of infinite-dimensional real Hilbert spaces. The strong and weak convergence theorems are obta...
In this paper, we establish coupled best proximity point theorems for multivalued mappings. Our results extend some recent results by Ali et al. (Abstr. Appl. Anal. 2014:181598, 2014) as well as other results in ...
In this paper, several kinds of generalized vector quasi-equilibrium problems are introduced and studied in abstract convex spaces. Using the properties of Γ-convex and
...
We prove the existence of fixed points of monotone-contraction mappings in modular function spaces. This is the modular version of the Ran and Reurings fixed point theorem. We also discus the extension of thes...
In this paper, we prove common coupled fixed point theorems under a Geraghty-type condition using monotone instead of the often used mixed monotone property. Also we give some sufficient conditions for the uni...
In 1994, Matthews obtained an extension of the celebrated Banach fixed point theorem to the partial metric framework (Ann. N.Y. Acad. Sci. 728:183-197, 1994). Motivated by the Matthews extension of the Banach ...
In this paper, we present a new iterative algorithm with errors to solve the problems of finding zeros of the sum of finitely many m-accretive operators and finitely many α-inversely strongly accretive operators ...
In this paper, we consider the set-valued contractions defined on product spaces when the underlying space is a complete metric space endowed with a graph. Some fixed point results for the so-called set-valued G-...
Let C be a nonempty, closed, and convex subset of a complete CAT(0) space X and let T be an asymptotically nonexpansive mapping of C into itself such that the set of common fixed points of T is nonempty. We intro...
The article is a continuation of the investigations concerning F-contractions which have been recently introduced in [Wardowski in Fixed Point Theory Appl. 2012:94,2012]. The authors extend the concept of F-contr...
In this paper, we consider the approximations of an iterative process for asymptotically k-strict pseudocontractive mappings in Hilbert spaces. Finally, we present some examples to study the rate of convergence.
The existence of the best proximity point for the proximal nonexpansive mapping on starshaped sets is studied. Our results are established without the assumptions of continuity, affinity or the P-property. Finall...
In this paper, the quasi-partial b-metric space is defined and general fixed point theorems on this space are discussed with examples.
First we present some interesting variants of Mann’s method. In the last section, we show that many existing results in the literature are concrete realizations of our general scheme under varying assumptions ...
In the present paper, we introduce a general iterative algorithm for finding a common element of the set of common fixed points of an infinite family of strict pseudo-contractions and the set of solutions of t...
In this paper, we establish the existence of fixed points for set-valued mappings satisfying certain graph contractions with set-valued domain endowed with a graph. These results unify, generalize, and complem...
In this paper, we consider an iterative algorithm for finding the common element of the set of solutions for the generalized mixed equilibrium problems, the common fixed points set of two generalized nonexpans...
In this paper, based on the viscosity approximation method and the regularized gradient-projection algorithm, we find a common element of the solution set of a constrained convex minimization problem and the s...
In this paper, we present a new proof of the Mazur-Orlicz theorem, which uses the Markov-Kakutani common fixed point theorem, and a new proof of the Markov-Kakutani common fixed point theorem, which uses the M...
The purpose of this paper is to introduce a new iteration by the combination of the viscosity approximation with Meir-Keeler contractions and proximal point algorithm for finding common zeros of a finite famil...
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