Related papers: Some results of fixed point of non-expansive mappi…
In this paper, a strong convergence theorem for asymptotically nonexpansive mappings in a uniformly convex and smooth Banach space is proved by using metric projections. This theorem extends and improves the recent strong convergence…
Some known fixed point theorems for nonexpansive mappings in metric spaces are extended here to the case of primitive uniform spaces. The reasoning presented in the proofs seems to be a natural way to obtain other general results.
This article generalizes the work of Ballmann and \'Swiatkowski to the case of Reflexive Banach spaces and uniformly convex Busemann spaces, thus giving a new fixed point criterion for groups acting on simplicial complexes.
We focus on the new type perturbed metric spaces and introduce a contraction mapping namely new type perturbed Kannan mappings. For these mappings, we show that Banach's fixed point theorem holds. Moreover, this new generalization of…
We establish fixed point theorems for nonlinear contractions on a metric space (not essentially complete) endowed with an arbitrary binary relation. Our results extend, generalize, modify and unify several known results especially those…
In this paper, we study the existence of fixed points for mappings defined on complete metric space (X, d) satisfying a general contractive inequality of integral type depended on another function. This conditions is analogous of Banach…
The aim of this paper is to establish a strong convergence theorem for a strongly nonexpansive sequence in a Banach space. We also deal with some applications of the convergence theorem.
Fixed point theory studies conditions under which nonexpansive maps on Banach spaces have fixed points. This paper examines the open question of whether every reflexive Banach space has the fixed point property. After surveying classical…
Based on the technique of enriching contractive type mappings, a technique that has been used successfully in some recent papers, we introduce the concept of {\it saturated} class of contractive mappings. We show that, from this…
In this paper, we introduce two new types of enriched contractions, viz., enriched $\mathcal{A}$-contraction and enriched $\mathcal{A}'$-contraction. Then we obtain fixed points of mappings satisfying such contractions using the fixed point…
We obtain results on the existence and approximation of fixed points of enriched contractions in quasi-Banach spaces and thus extend the results obtained in the case of contractions defined on Banach spaces [Berinde, V.; P\u{a}curar, M.…
Banach's fixed point theorem in linear n-normed space is being developed. Also, we present several theorems on fixed points in linear n-normed space.
The main result of this paper is a fixed point result relating the spreading model structure of Banach spaces and Schauder basis with not too large basis constant. As a striking consequence, we deduce that every super-reflexive space has…
In this paper, a general hybrid fixed point theorem for the contractive mappings in generalized Banach spaces is proved via measure of weak non-compactness and it is further applied to fractional integral equations for proving the existence…
We survey several applications of fixed point theorems in the theory of invariant subspaces. The general idea is that a fixed point theorem applied to a suitable map yields the existence of invariant subspaces for an operator on a Banach…
Cyclic contractions generalize the usual contractivities in metric spaces and $b$-MSs. In this paper, we enhance several fixed point theorems related to cyclic (i) Banach self-maps, (ii) Chatterjea contractivities, (iii) Kannan…
In this article we extend the notion of orthogonal metric space to weak orthogonal metric space. Then we establish fixed point results for a mapping satisfying a more general contraction condition. Several nontrivial examples are given in…
In this paper, we investigate the existence of fixed points for asymptotically nonexpansive mappings with center 0 defined on closed convex subsets of various Banach spaces. Three applications are given. Firstly, we prove that our results…
Alternative iterative methods for a nonexpansive mapping in a Banach space are proposed and proved to be convergent to a common solution to a fixed point problem and a variational inequality. We give rates of asymptotic regularity for such…
In this work, using a new geometrical approach we study to the existence of the fixed-point of mappings that independence of the smoothness, and also of their single-values or multi-values. This work proved the theorems that generalize in…