Convergence of iterates of nonexpansive mappings and orbits of nonexpansive semigroups

2019 ◽  
Vol 475 (1) ◽  
pp. 519-531 ◽  
Author(s):  
Aleksandra Grzesik ◽  
Wiesława Kaczor ◽  
Tadeusz Kuczumow ◽  
Simeon Reich
Keyword(s):  
Nonexpansive Mappings ◽  
Nonexpansive Semigroups

scholarly journals Common fixed points of one-parameter nonexpansive semigroups in strictly convex Banach spaces

2006 ◽  
Vol 2006 ◽  
pp. 1-10 ◽  
Author(s):  
Tomonari Suzuki
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Convex Subset ◽  
Continuous Semigroup ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Strongly Continuous Semigroup ◽  
Nonexpansive Semigroups ◽  
Semigroup Of Nonexpansive Mappings ◽  
Strictly Convex Banach Spaces

One of our main results is the following convergence theorem for one-parameter nonexpansive semigroups: letCbe a bounded closed convex subset of a Hilbert spaceE, and let{T(t):t∈ℝ+}be a strongly continuous semigroup of nonexpansive mappings onC. Fixu∈Candt1,t2∈ℝ+witht1<t2. Define a sequence{xn}inCbyxn=(1−αn)/(t2−t1)∫t1t2T(s)xnds+αnuforn∈ℕ, where{αn}is a sequence in(0,1)converging to0. Then{xn}converges strongly to a common fixed point of{T(t):t∈ℝ+}.

scholarly journals Implicit Ishikawa Approximation Methods for Nonexpansive Semigroups in CAT(0) Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Zhi-bin Liu ◽  
Yi-shen Chen ◽  
Xue-song Li ◽  
Yi-bin Xiao
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Nonexpansive Mappings ◽  
Nonexpansive Semigroup ◽  
Approximation Methods ◽  
Ishikawa Iteration ◽  
Nonexpansive Semigroups ◽  
Convergence Results ◽  
Iteration Processes

This paper is devoted to the convergence of the implicit Ishikawa iteration processes for approximating a common fixed point of nonexpansive semigroup in CAT(0) spaces. We obtain theΔ-convergence results of the implicit Ishikawa iteration sequences for a family of nonexpansive mappings in CAT(0) spaces. Under certain and different conditions, we also get the strong convergence theorems of implicit Ishikawa iteration sequences for nonexpansive semigroups in the CAT(0) spaces. The results presented in this paper extend and generalize some previous results.

Iterative algorithm for a split equilibrium problem and fixed problem for finite asymptotically nonexpansive mappings in Hlbert space

Filomat ◽  
2017 ◽  
Vol 31 (5) ◽  
pp. 1423-1434 ◽  
Author(s):  
Sheng Wang ◽  
Min Chen
Keyword(s):  
Equilibrium Problem ◽  
Iterative Algorithm ◽  
Nonexpansive Mappings ◽  
Common Element ◽  
Fixed Point Set ◽  
Split Equilibrium Problem ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Point Set ◽  
The Common

In this paper, we propose an iterative algorithm for finding the common element of solution set of a split equilibrium problem and common fixed point set of a finite family of asymptotically nonexpansive mappings in Hilbert space. The strong convergence of this algorithm is proved.

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