scholarly journals Cascading Operators in CAT(0) Spaces

Axioms ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 20
Author(s):  
Helga Fetter Nathansky ◽  
Jeimer Villada Bedoya
Keyword(s):  
Convergence Theorem ◽  
Metric Spaces ◽  
Iteration Process ◽  
Mann Iteration ◽  
Expansive Maps ◽  
Mann Iteration Process

In this work, we introduce the notion of cascading non-expansive mappings in the setting of CAT(0) spaces. This family of mappings properly contains the non-expansive maps, but it differs from other generalizations of this class of maps. Considering the concept of Δ-convergence in metric spaces, we prove a principle of demiclosedness for this type of mappings and a Δ-convergence theorem for a Mann iteration process defined using cascading operators.

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 Fibonacci–Mann Iteration for Monotone Asymptotically Nonexpansive Mappings in Modular Spaces

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 481 ◽  
Author(s):  
Buthinah Dehaish ◽  
Mohamed Khamsi
Keyword(s):  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Modular Function ◽  
Function Spaces ◽  
Mann Iteration ◽  
Modular Spaces ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Modular Function Spaces ◽  
Mann Iteration Process

In this work, we extend the fundamental results of Schu to the class of monotone asymptotically nonexpansive mappings in modular function spaces. In particular, we study the behavior of the Fibonacci–Mann iteration process, introduced recently by Alfuraidan and Khamsi, defined by

scholarly journals Fibonacci-Mann Iteration for Monotone Asymptotically Nonexpansive Mappings in Modular Spaces

2018 ◽  
Author(s):  
Buthinah A. Bin Dehaish ◽  
Mohamed A Khamsi
Keyword(s):  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Modular Function ◽  
Function Spaces ◽  
Mann Iteration ◽  
Modular Spaces ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Modular Function Spaces ◽  
Mann Iteration Process

In this work, we extend the fundamental results of Schu to the class of monotone asymptotically nonexpansive mappings in modular function spaces. In particular, we study the behavior of the Fibonacci-Mann iteration process defined by $$x_{n+1} = t_n T^{\phi(n)}(x_n) + (1-t_n)x_n,$$ for $n \in \mathbb{N}$, when $T$ is a monotone asymptotically nonexpansive self-mapping.

scholarly journals Approximating Common Fixed Points of an Evolution Family on a Metric Space via Mann Iteration

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Liang Luo ◽  
Rizwan Ullah ◽  
Gul Rahmat ◽  
Saad Ihsan Butt ◽  
Muhammad Numan
Keyword(s):  
Fixed Points ◽  
Metric Space ◽  
Irrational Number ◽  
Iteration Process ◽  
Common Fixed Points ◽  
Evolution Family ◽  
Mann Iteration ◽  
The Family ◽  
Families Of Operators ◽  
Mann Iteration Process

In this article, we present the set of all common fixed points of a subfamily of an evolution family in terms of intersection of all common fixed points of only two operators from the family; that is, for subset M of L , we have F M = F Y ϱ 1 , 0 ∩ F Y ϱ 2 , 0 , where ϱ 1 and ϱ 2 are positive and ϱ 1 / ϱ 2 is an irrational number. Furthermore, we approximate such common fixed points by using the modified Mann iteration process. In fact, we are generalizing the results from a semigroup of operators to evolution families of operators on a metric space.

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.

scholarly journals On New Picard-Mann Iterative Approximations with Mixed Errors for Implicit Midpoint Rule and Applications

2019 ◽  
Vol 2019 ◽  
pp. 1-13
Author(s):  
Teng-fei Li ◽  
Heng-you Lan
Keyword(s):  
Optimal Control Problems ◽  
Nonexpansive Mappings ◽  
Elliptic Boundary ◽  
Iteration Process ◽  
Implicit Midpoint Rule ◽  
Mann Iteration ◽  
Midpoint Rule ◽  
Elliptic Boundary Value ◽  
Mann Iteration Process ◽  
Iteration Processes

In order to solve (partial) differential equations, implicit midpoint rules are often employed as a powerful numerical method. The purpose of this paper is to introduce and study a class of new Picard-Mann iteration processes with mixed errors for the implicit midpoint rules, which is different from existing methods in the literature, and to analyze the convergence and stability of the proposed method. Further, some numerical examples and applications to optimal control problems with elliptic boundary value constraints are considered via the new Picard-Mann iterative approximations, which shows that the new Picard-Mann iteration process with mixed errors for the implicit midpoint rule of nonexpansive mappings is brand new and more effective than other related iterative processes.

Sign in / Sign up

Export Citation Format

Share Document