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Let
be a real uniformly convex Banach space which admits a weakly sequentially continuous duality mapping from
...
We prove a fixed point theorem for weakly compatible maps satisfying a general contractive condition of integral type.
Let
be a bounded, convex domain in
, and suppose that
The continuation principle for generalized contractions in gauge spaces is used to discuss nonlinear integral equations with advanced argument.
We modified the classic Mann iterative process to have strong convergence theorem for a finite family of nonexpansive mappings in the framework of Hilbert spaces. Our results improve and extend the results ann...
We obtain several fixed point theorems for hybrid pairs of single-valued and multivalued occasionally weakly compatible maps defined on a symmetric space satisfying a contractive condition of integral type. Th...
The Erratum to this article has been published in Fixed Point Theory and Applications 2008 2008:274793
-Metric Spaces
We give some new definitions of
-metric spaces and we prove a common fixed point theorem for a class of mappings under the condition of ...
-Accretive Operators
We introduce and study a new system of variational inclusions with
-accretive operators, which contains variational inequalities, variat...
We prove the Hyers-Ulam-Rassias stability of homomorphisms in real Banach algebras and of generalized derivations on real Banach algebras for the following Cauchy-Jensen functional equations: ...
We show that the convergence of Picard iteration is equivalent to the convergence of Mann iteration schemes for various Zamfirescu operators. Our result extends of Soltuz (2005).
Strong and weak convergence theorems for multistep iterative scheme with errors for finite family of asymptotically nonexpansive mappings are established in Banach spaces. Our results extend and improve the co...
Some properties of the linear continuous operator and separation of convex subsets are investigated in this paper and a dual space for a subspace of a reflexive Banach space with a strictly convex norm is cons...
-Lipschitzian Mappings in Banach Spaces
The purpose of this paper is to prove a strong convergence theorem for a finite family of uniformly
-Lipschitzian mappings in Banach spa...
We will apply the fixed point method for proving the Hyers-Ulam-Rassias stability of a Volterra integral equation of the second kind.
Diametrically contractive mappings on a complete metric space are introduced by V. I. Istratescu. We extend and generalize this idea to multivalued mappings. An easy example shows that our fixed point theorem ...
Let
be a nonempty subset (not necessarily closed and convex) of a Hilbert space and let
...
Suppose that
is a nonempty closed convex subset of a real uniformly convex and smooth Banach space
...
We discuss weakly contractive maps on complete metric spaces. Following three methods of generalizing the Banach contraction principle, we obtain some fixed point theorems under some relatively weaker and more...
-Mapping on
-Convex Spaces
We establish some coincidence theorems, generalized variational inequality theorems, and minimax inequality theorems for the family
-KKM...
Motivated by T. Suzuki, we show strong convergence theorems of the CQ method for nonexpansive semigroups in Hilbert spaces by hybrid method in the mathematical programming. The results presented extend and imp...
Strong convergence theorems are obtained by hybrid method for modified composite implicit iteration process of nonexpansive mappings in Hilbert spaces. The results presented in this paper generalize and improv...
The convex feasibility problem (CFP) of finding a point in the nonempty intersection
is considered, where
...
-Contractive Mappings in Fuzzy Metric Spaces
We answer into affirmative an open question raised by A. Razani in 2005. An essential role in our proofs is played by the separation axiom in the definition of a fuzzy metric space in the sense of George and V...
We propose an iteration scheme with perturbed mapping for approximation of common fixed points of a finite family of nonexpansive mappings
Let
be a closed convex subset of a complete metrizable topological vector space
...
Let
and
be
...
The purpose of this paper is to present several existence and data dependence results of the fixed points of some multivalued generalized contractions in complete metric spaces. As for application, a continuat...
We first introduce and analyze an algorithm of approximating solutions of maximal monotone operators in Hilbert spaces. Using this result, we consider the convex minimization problem of finding a minimizer of ...
Let
be an arbitrary real Banach space and
a nonempty, clos...
Using the convex combination based on Bregman distances due to Censor and Reich, we define an operator from a given family of relatively nonexpansive mappings in a Banach space. We first prove that the fixed-p...
In real Hilbert space
, from an arbitrary initial point
, an...
We provide sufficient conditions for the iterates of an asymptotic contraction on a complete metric space
to converge to its unique fix...
The existence of fixed points for single or multivalued mappings is obtained as a corollary of Nash equilibrium existence in finitely many players games.
We introduce methods which seem to be a new and promising tool in hierarchical fixed-point problems. The goal of this note is to analyze the convergence properties of these new types of approximating methods f...
We will establish sufficient conditions for the existence of integral solutions and extremal integral solutions for semilinear functional differential equations with nondensely defined operators in Banach spaces.
We introduce an iteration scheme for nonexpansive mappings in a Hilbert space and prove that the iteration converges strongly to common fixed points of the mappings without commutativity assumption.
The aim of this erratum is to make necessary corrections in the proof of Theorem 2.1 of Babu and Prasad (2006).
The original article was published in Fixed Point Theory and Applications 2006 2006:49615
This paper presents a remark on a fixed point theorem of Krasnosel'skii type. This result is applied to prove the existence of asymptotically stable solutions of nonlinear integral equations.
The purpose of this paper is to study the weak and strong convergence of implicit iteration process with errors to a common fixed point for a finite family of nonexpansive mappings in Banach spaces. The result...
We discuss convergence theorems of modified Ishikawa and Mann iterative sequences with errors for asymptotically pseudocontractive and asymptotically nonexpansive mappings in Banach spaces, and the boundedness...
-accretive operators
Let
be a real reflexive Banach space, let
be a closed conv...
Strong convergence theorems are obtained from modified Halpern iterative scheme for asymptotically nonexpansive mappings and asymptotically nonexpansive semigroups, respectively. Our results extend and improve...
We prove an almost coincidence point theorem in generalized convex spaces. As an application, we derive a result on the existence of a maximal element and an almost coincidence point theorem in hyperconvex spa...
Contractive maps have nice properties concerning fixed points; a big amount of literature has been devoted to fixed points of nonexpansive maps. The class of shrinking (or strictly contractive) maps is slightl...
The topological approaches to find solutions of a coincidence equation
can roughly be divided into degree and index theories. We descri...
-closure points of ultimately nonexpansive mappings
Let
be a closed subset of a Banach space and
an ultimately...
We are concerned with the study of a multistep iterative scheme with errors involving a finite family of nonexpansive nonself-mappings. We approximate the common fixed points of a finite family of nonexpansive...
Using the concept of
-
-proximal mapping, we study the existence and sensiti...
The purpose of this paper is to study sufficient and necessary conditions for finite-step iterative sequences with mean errors for a finite family of asymptotically quasi-nonexpansive and type mappings in Bana...
Let
be a nonempty closed convex subset of a smooth Banach space
and let
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