Related papers: On a novel approach to nonexpansive mappings
In this paper, we introduce a new type of coupled fixed point theorem in partially ordered complete metric space. We give an example to support of our result.
This study first defines a new metric with normal structure on C(H,K) and then a new technique to prove fixed point theorems for families of non-expansive maps on this metric space. Indeed, it shows that the presence of a bounded orbit…
We consider bounded 2-metric spaces satisfying an additional axiom, and show that a contractive mapping has either a fixed point or a fixed line.
We consider fixed-point models for topological phases of matter formulated as discrete path integrals in the language of tensor networks. Such zero-correlation length models with an exact notion of topological invariance are known in the…
Let $(A, B)$ be a nonempty bounded closed convex proximal parallel pair in a nearly uniformly convex Banach space and $T: A\cup B \rightarrow A\cup B$ be a continuous and asymptotically relatively nonexpansive map. We prove that there…
Iterative algorithms are fundamental tools for approximating fixed-points of nonexpansive operators in real Hilbert spaces. Among them, Krasnosel'ski\u{\i}--Mann iteration and Halpern iteration are two widely used schemes. In this work, we…
Let $X$ be a metric space. Recently in~[1] it was considered a new type of mappings $T\colon X\to X$ which can be characterized as mappings contracting perimeters of triangles. These mappings are defined by the condition based on the…
In this paper, we present some common fixed point theorems for a commuting pair of mappings, including a generalized nonexpansive single valued mapping and a generalized nonexpansive multivalued mapping in strictly convex Banach spaces. The…
Among other results, the paper gives new mapping theorems and new fixed point property theorems for inverse limits of inverse sequences of compact metric spaces with upper semicontinuous set-valued bonding functions. We also revisit the…
Our aim in this paper is to prove some interesting fixed point theorems for the class of asymptotically $T$-regular mappings in the framework of preordered modular G-metric spaces. Our results are novel and generalizes several know results.…
The major motives of this paper are to study different types of contractive mappings and also to answer an open question of Garai et al. [The contractive principle for mappings in $b_v(s)$-metric spaces, arXiv:1802.03136]. We first set up…
In this paper we study fixed point properties for semitopological semigroup of nonexpansive mappings on a bounded closed convex subset of a Banach space. We also study a Schauder fixed point property for a semitopological semigroup of…
In this paper, we first introduce an iterative process in modular function spaces and then extend the idea of a {\lambda}-firmly nonexpansive mapping from Banach spaces to modular function spaces. We call such mappings as…
A new, simple and unified approach in the theory of contractive mappings was recently given by Samet \emph{et al.} (Nonlinear Anal. 75, 2012, 2154-2165) by using the concepts of $\alpha$-$\psi$-contractive type mappings and…
In this paper, two-to-one mappings and involutions without any fixed point on finite fields of even characteristic are investigated. First, we characterize a closed relationship between them by implicit functions and develop an AGW-like…
It is shown that if $S$ is a commuting family of weak$^{\ast }$ continuous nonexpansive mappings acting on a weak$^{\ast }$ compact convex subset $C$ of the dual Banach space $E$, then the set of common fixed points of $S$ is a nonempty…
We introduce and investigate an iterative scheme for approximating common fixed point of a family of Bregman relatively-nonexpansive mappings in real reflexive Banach spaces. We prove strong convergence theorem of the sequence generated by…
In this study, we introduce a new iterative processes to approximate common fixed points of an infinite family of quasi-nonexpansive mappings and obtain a strongly convergent iterative sequence to the common fixed points of these mappings…
In this work, we suggest a general viscosity implicit midpoint rule for nonexpansive mapping in the framework of Hilbert space. Further, under the certain conditions imposed on the sequence of parameters, strong convergence theorem is…
The paper introduces the class of O-metric spaces, a novel generalization of metric-type spaces, classifying almost all possible metric types into upward and downward O-metrics. We list some topologies arising from O-metrics and discuss…