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-Accretive Framework
A general nonlinear framework for an Ishikawa-hybrid proximal point algorithm using the notion of
-accretive is developed. Convergence a...
We introduce an iterative scheme by the viscosity iterative method for finding a common element of the solution set of an equilibrium problem, the solution set of the variational inequality, and the fixed poin...
We introduce a new iterative scheme for finding a common element of infinitely nonexpansive mappings, the set of solutions of a mixed equilibrium problems, and the set of solutions of the variational inequalit...
We first introduce the new concept of a distance called
-distance, which generalizes
...
We obtain common fixed points of a pair of mappings satisfying a generalized contractive type condition in TVS-valued cone metric spaces. Our results generalize some well-known recent results in the literature.
In recent years, the definition of weak relatively nonexpansive mapping has been presented and studied by many authors. In this paper, we give some results about weak relatively nonexpansive mappings and give ...
-Maps in
-Metric Spaces
We prove some fixed point results for self-mapping
in a complete
Let
be N strict pseudocontractions defined on a closed convex subset
-Trees
It is proved that a complete geodesically bounded
-tree is the closed convex hull of the set of its extreme points. It is also noted tha...
We discuss the newly introduced concept of cone metric spaces. We also discuss the fixed point existence results of contractive mappings defined on such metric spaces. In particular, we show that most of the n...
First the characteristic of monotonicity of any Banach lattice
is expressed in terms of the left limit of the modulus of monotonicity of
Coincidence and fixed point theorems for a new class of contractive, nonexpansive and hybrid contractions are proved. Applications regarding the existence of common solutions of certain functional equations ar...
The existence of approximate fixed points and approximate endpoints of the multivalued almost
-contractions is established. We also develop quan...
A method based on the Banach fixed-point theorem is proposed for obtaining certain solutions (TE-polarized electromagnetic waves) of the Helmholtz equation describing the reflection and transmission of a plane...
We extend a common fixed point theorem of Radenovic and Rhoades for four non-self-mappings in cone metric spaces.
We prove some fixed point theorems for multivalued maps in cone metric spaces. We improve and extend a number of known fixed point results including the corresponding recent fixed point results of Feng and Liu...
We discuss fixed point properties of convex subsets of locally convex linear topological spaces. We derive equivalence among fixed point properties concerning several types of multivalued mappings.
We present some new critical point theorems for nonlinear dynamical systems which are generalizations of Dancš-Hegedüs-Medvegyev's principle in uniform spaces and metric spaces by applying an abstract maximal ...
Let
be an open subset and
be an arbitrary local homeomorph...
Let
be a real Banach space with the dual space
. Let
...
We consider another class of generalized Lipschitzian type mappings and utilize the same to prove fixed point theorems for asymptotically regular and uniformly generalized Lipschitzian one-parameter semigroups...
-Accretive Mappings
The main purpose of this paper is to introduce and study a new class of generalized nonlinear set-valued quasi-variational inclusions system involving
The purpose of this paper is to present a fixed point theorem for generalized contractions in partially ordered complete metric spaces. We also present an application to first-order ordinary differential equat...
Given a tangent vector field on a finite-dimensional real smooth manifold, its degree (also known as characteristic or rotation) is, in some sense, an algebraic count of its zeros and gives useful information for...
This paper is devoted to the investigation of the existence of fixed points in a normed linear space
endowed with a norm
We prove some theorems for the existence of ergodic retractions onto the set of common fixed points of a family of asymptotically nonexpansive mappings. Our results extend corresponding results of Benavides an...
Our aim is twofold: first, we want to introduce a partial quasiordering in cone uniform spaces with generalized pseudodistances for giving the general maximality principle in these spaces. Second, we want to s...
The partial KKM principle for an abstract convex space is an abstract form of the classical KKM theorem. In this paper, we derive generalized forms of the Ky Fan minimax inequality, the von Neumann-Sion minima...
Using fixed point methods, we prove the Hyers-Ulam-Rassias stability of a mixed type functional equation on multi-Banach spaces.
We discuss the dynamic traffic network equilibrium system problem. We introduce the equilibrium definition based on Wardrop's principles when there are some internal relationships between different kinds of go...
We introduce an iterative method for a pair of hemirelatively nonexpansive mappings. Strong convergence of the purposed iterative method is obtained in a Banach space.
The main aim of this paper is to study and establish some new coupled fixed point theorems for nonlinear contractive maps that satisfied Mizoguchi-Takahashi's condition in the setting of quasiordered metric sp...
A new nonlinear mapping is introduced. The convergence of Ishikawa iterative processes for the class of asymptotically pseudocontractive mappings in the intermediate sense is studied. Weak convergence theorems...
Existence theorems of fixed points for multivalued increasing operators in partially ordered spaces are presented. Here neither the continuity nor compactness is assumed for multivalued operators. As an applic...
We prove common fixed point theorem for coincidentally commuting nonself mappings satisfying generalized contraction condition of Ćirić type in cone metric space. Our results generalize and extend all the rece...
In 1957, Kolmogorov and Arnold gave a solution to the 13th problem which had been formulated by Hilbert in 1900. Actually, it is known that there exist many open problems which can be derived from the original...
We prove that the set of common fixed points of a given countable family of relatively nonexpansive mappings is identical to the fixed-point set of a single strongly relatively nonexpansive mapping. This answe...
Hyperbolic toral automorphisms provide important examples of chaotic dynamical systems. Generalizing automorphisms on tori, we study (infra-)nil endomorphisms defined on (infra-)nilmanifolds. In particular, we...
In 1965, Kirk proved that if
is a nonempty weakly compact convex subset of a Banach space with normal structure, then every nonexpansiv...
Some mutual relations between p-cyclic contractive self-mappings, p-cyclic Kannan self-mappings, and Meir-Keeler p-cyclic contractions are stated. On the other hand, related results about the existence of the bes...
-Pair Mappings on Cone Metric Spaces
We define the concept of generalized
-pair mappings and prove some common fixed point theorems for this type of mappings. Our results ge...
We are going to answer some open questions in the theory of hyperconvex metric spaces. We prove that in complete
-trees hyperconvex hull...
The aim of this paper is to obtain some existence theorems related to a hybrid projection method and a hybrid shrinking projection method for firmly nonexpansive-like mappings (mappings of type (P)) in a Banac...
We define a new concept of integral with respect to a cone. Moreover, certain fixed point theorems in those spaces are proved. Finally, an extension of Meir-Keeler fixed point in cone metric space is proved.
The Erratum to this article has been published in Fixed Point Theory and Applications 2011 2011:346059
-Fuzzy Metric Spaces
We introduce partially ordered
-fuzzy metric spaces and prove a common fixed point theorem in these spaces.
Kirk and Saliga and then Chen et al. introduced lower semicontinuity from above, a generalization of sequential lower semicontinuity, and they showed that well-known results, such as Ekeland's variational prin...
We establish fixed point theorems for multivalued mappings defined on a closed subset of a complete metric space. We generalize Lim's result on weakly inward contractions in a Banach space. We also generalize ...
We introduce composite iterative schemes by the viscosity iteration method for finding a zero of an accretive operator in reflexive Banach spaces. Then, under certain differen control conditions, we establish ...
We propose some new iterative schemes for finding common fixed point of an infinite family of nonexpansive mappings in a Hilbert space and prove the strong convergence of the proposed schemes. Our results exte...
We first give some fixed point results for set-valued self-map contractions in complete metric spaces. Then we derive a fixed point theorem for nonself set-valued contractions which are metrically inward. Our ...
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