scholarly journals Approximating common fixed points of two asymptotically quasi-nonexpansive mappings in Banach spaces

2010 ◽  
Vol 42 (1) ◽  
pp. 19-30
Author(s):  
Isa Yildirim ◽  
Murat Özdemir
Keyword(s):  
Weak Convergence ◽  
Fixed Points ◽  
Banach Spaces ◽  
Iterative Algorithm ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Uniformly Convex ◽  
Convergence Theorems ◽  
Strong And Weak Convergence ◽  
Uniformly Convex Banach Spaces

In this paper, we consider a composite iterative algorithm for approximating common fixed points of two nonself asymptotically quasi-nonexpansive mappings and we prove some strong and weak convergence theorems for such mappings in uniformly convex Banach spaces.

scholarly journals Common fixed points of two finite families of nonexpansive mappings by iterations

2015 ◽  
Vol 31 (3) ◽  
pp. 325-331
Author(s):  
HAFIZ FUKHAR-UD-DIN ◽  
◽  
Keyword(s):  
Strong Convergence ◽  
Fixed Points ◽  
Banach Spaces ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Uniformly Convex ◽  
Convergence Theorems ◽  
Uniformly Convex Banach Spaces

We study a Mann type iterative scheme for two finite families of nonexpansive mappings and establish 4− convergence and strong convergence theorems. The obtained results are applicable in uniformly convex Banach spaces (linear domain) and CAT (0) spaces (nonlinear domain) simultaneously.

scholarly journals Some Convergence Results for a Class of Generalized Nonexpansive Mappings in Banach Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Thabet Abdeljawad ◽  
Kifayat Ullah ◽  
Junaid Ahmad ◽  
Manuel de la Sen ◽  
Muhammad Naveed Khan
Keyword(s):  
Weak Convergence ◽  
Iterative Method ◽  
Fixed Points ◽  
Banach Spaces ◽  
Current Literature ◽  
Nonexpansive Mappings ◽  
Uniformly Convex ◽  
Strong And Weak Convergence ◽  
Convergence Results ◽  
Uniformly Convex Banach Spaces

This paper investigates fixed points of Reich-Suzuki-type nonexpansive mappings in the context of uniformly convex Banach spaces through an M ∗ iterative method. Under some appropriate situations, some strong and weak convergence theorems are established. To support our results, a new example of Reich-Suzuki-type nonexpansive mappings is presented which exceeds the class of Suzuki-type nonexpansive mappings. The presented results extend some recently announced results of current literature.

Two-step iterative approximation of common fixed points of two nonself asymptotically quasi-nonexpansive mappings

2015 ◽  
Vol 08 (03) ◽  
pp. 1550060
Author(s):  
Amit Singh ◽  
R. C. Dimri ◽  
Darshana J. Prajapati
Keyword(s):  
Banach Space ◽  
Weak Convergence ◽  
Fixed Points ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Convex Banach Space ◽  
Uniformly Convex ◽  
Iterative Approximation ◽  
Convergence Theorems ◽  
Strong And Weak Convergence

In this paper, we study an iterative approximation of common fixed points of two nonself asymptotically quasi-nonexpansive mappings and we prove some strong and weak convergence theorems for such mappings in a uniformly convex Banach space.

scholarly journals Common Fixed Points of Two G -Nonexpansive Mappings via a Faster Iteration Procedure

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Sabiya Khatoon ◽  
Izhar Uddin ◽  
Javid Ali ◽  
Reny George
Keyword(s):  
Fixed Points ◽  
Banach Spaces ◽  
Directed Graph ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Iteration Procedure ◽  
Uniformly Convex ◽  
Numerical Example ◽  
Uniformly Convex Banach Spaces

In this work, we study the convergence of a new faster iteration in which two G -nonexpansive mappings are involved in the setting of uniformly convex Banach spaces with a directed graph. Moreover, by constructing a numerical example, we show the fastness of our iteration procedure over other existing iteration procedures in the literature.

scholarly journals Common Fixed Points of Two Generalized Asymptotically Quasi-Nonexpansive Mappings

2015 ◽  
Vol 0 (0) ◽  
Author(s):  
Safeer Hussain Khan ◽  
Isa Yildirim
Keyword(s):  
Weak Convergence ◽  
Fixed Points ◽  
Iterative Procedure ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Convergence Theorems ◽  
Strong And Weak Convergence

Abstract In this paper, we consider an iterative procedure for approximating common fixed points of two generalized asymptotically quasi-nonexpansive mappings and we prove some strong and weak convergence theorems for such mappings in uniformly con- vex Banach spaces.This will extend the results of Cholamjiak and Suantai, Khan and those generalized therein to the case of generalized asymptotically quasi-nonexpansive mappings and by a faster iterative procedure.

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