scholarly journals Fixed points of Osilike-Berinde-G-nonexpansive mappings in metric spaces endowed with graphs

2021 ◽  
Vol 37 (2) ◽  
pp. 311-323
Author(s):  
A. KAEWKHAO ◽  
C. KLANGPRAPHAN ◽  
B. PANYANAK
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Nonexpansive Mapping ◽  
Metric Spaces ◽  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Fixed Point Set ◽  
Quasinonexpansive Mapping ◽  
Ishikawa Iteration Process ◽  
Point Set

"In this paper, we introduce the notion of Osilike-Berinde-G-nonexpansive mappings in metric spaces and show that every Osilike-Berinde-G-nonexpansive mapping with nonempty fixed point set is a G-quasinonexpansive mapping. We also prove the demiclosed principle and apply it to obtain a fixed point theorem for Osilike-Berinde-G-nonexpansive mappings. Strong and \Delta-convergence theorems of the Ishikawa iteration process for G-quasinonexpansive mappings are also discussed."

scholarly journals A Mean Ergodic Theorem for Affine Nonexpansive Mappings in Nonpositive Curvature Metric Spaces

2021 ◽  
Vol 29 (1) ◽  
pp. 111-125
Author(s):  
Hadi Khatibzadeh ◽  
Hadi Pouladi
Keyword(s):  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Ergodic Theorem ◽  
Tauberian Theorem ◽  
Metric Spaces ◽  
Nonexpansive Mappings ◽  
Nonpositive Curvature ◽  
Fixed Point Set ◽  
Von Neumann ◽  
Point Set

Abstract In this paper, we consider the orbits of an affine nonexpansive mapping in Hadamard (nonpositive curvature metric) spaces and prove an ergodic theorem for the inductive mean, which extends the von Neumann linear ergodic theorem. The main result shows that the sequence given by the inductive means of iterations of an affine nonexpansive mapping with a nonempty fixed point set converges strongly to a fixed point of the mapping. A Tauberian theorem is also proved in order to ensure convergence of the iterations.

Goebel and Kirk fixed point theorem for multivalued asymptotically nonexpansive mappings

2017 ◽  
Vol 33 (3) ◽  
pp. 335-342
Author(s):  
M. A. KHAMSI ◽  
◽  
A. R. KHAN ◽  
◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Nonexpansive Mapping ◽  
Point Theorem ◽  
Metric Spaces ◽  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Mann Iteration ◽  
Asymptotically Nonexpansive ◽  
Mann Iteration Process

We introduce the concept of a multivalued asymptotically nonexpansive mapping and establish Goebel and Kirk fixed point theorem for these mappings in uniformly hyperbolic metric spaces. We also define a modified Mann iteration process for this class of mappings and obtain an extension of some well-known results for singlevalued mappings defined on linear as well as nonlinear domains.

scholarly journals On convergence theorems for single-valued and multi-valued mappings in p-uniformly convex metric spaces

2021 ◽  
Vol 37 (3) ◽  
pp. 513-527
Author(s):  
JENJIRA PUIWONG ◽  
◽  
SATIT SAEJUNG ◽  
◽  
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Nonexpansive Mappings ◽  
Iterative Sequence ◽  
Uniformly Convex ◽  
Fixed Point Set ◽  
Convergence Theorems ◽  
Convex Metric Spaces ◽  
Strict Fixed Point ◽  
Point Set

We prove ∆-convergence and strong convergence theorems of an iterative sequence generated by the Ishikawa’s method to a fixed point of a single-valued quasi-nonexpansive mappings in p-uniformly convex metric spaces without assuming the metric convexity assumption. As a consequence of our single-valued version, we obtain a result for multi-valued mappings by showing that every multi-valued quasi-nonexpansive mapping taking compact values admits a quasi-nonexpansive selection whose fixed-point set of the selection is equal to the strict fixed-point set of the multi-valued mapping. In particular, we immediately obtain all of the convergence theorems of Laokul and Panyanak [Laokul, T.; Panyanak, B. A generalization of the (CN) inequality and its applications. Carpathian J. Math. 36 (2020), no. 1, 81–90] and we show that some of their assumptions are superfluous.

scholarly journals Common Fixed-Point Problem for a Family Multivalued Mapping in Banach Space

2011 ◽  
Vol 2011 ◽  
pp. 1-9
Author(s):  
Zhanfei Zuo
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Nonexpansive Mappings ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Fixed Point Set ◽  
Common Fixed Point Problem ◽  
The Family ◽  
Point Set ◽  
The Common

It is our purpose in this paper to prove two convergents of viscosity approximation scheme to a common fixed point of a family of multivalued nonexpansive mappings in Banach spaces. Moreover, it is the unique solution in to a certain variational inequality, where stands for the common fixed-point set of the family of multivalued nonexpansive mapping .

scholarly journals Mann iteration process for monotone nonexpansive mappings with a graph

2019 ◽  
Vol 26 (4) ◽  
pp. 629-636
Author(s):  
Monther Rashed Alfuraidan
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Convex Subset ◽  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Mann Iteration ◽  
Iteration Sequence ◽  
Mann Iteration Process ◽  
Monotone Nonexpansive Mapping

Abstract Let {(X,\lVert\,\cdot\,\rVert)} be a Banach space. Let C be a nonempty, bounded, closed and convex subset of X and let {T:C\rightarrow C} be a G-monotone nonexpansive mapping. In this work, it is shown that the Mann iteration sequence defined by x_{n+1}=t_{n}T(x_{n})+(1-t_{n})x_{n},\quad n=1,2,\dots, proves the existence of a fixed point of G-monotone nonexpansive mappings.

Examples and Questions in the Theory of Fixed Point Sets

1979 ◽  
Vol 31 (5) ◽  
pp. 1017-1032 ◽  
Author(s):  
John R. Martin ◽  
Sam B. Nadler
Keyword(s):  
Fixed Point ◽  
Continuous Function ◽  
Banach Spaces ◽  
Metric Spaces ◽  
Compact Manifolds ◽  
Invariance Property ◽  
Point Sets ◽  
Fixed Point Set ◽  
Point Set ◽  
Fixed Point Sets

All spaces considered in this paper will be metric spaces. A subset A of a space X is called a fixed point set of X if there is a map (i.e., continuous function) ƒ: X → X such that ƒ(x) = x if and only if x ∈ A. In [22] L. E. Ward, Jr. defines a space X to have the complete invariance property (CIP) provided that each of the nonempty closed subsets of X is a fixed point set of X. The problem of determining fixed point sets of spaces has been investigated in [14] through [20] and [22]. Some spaces known to have CIP are n-cells[15], dendrites [20], convex subsets of Banach spaces [22], compact manifolds without boundary [16], and a class of polyhedra which includes all compact triangulable manifolds with or without boundary [18].

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