Strong convergence theorems of common fixed point for asymptotically quasi-nonexpansive type mappings in convex metric spaces

2013 ◽  
Vol 4 (4) ◽  
pp. 28
Author(s):  
G. S. Saluja
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Metric Spaces ◽  
Convergence Theorems ◽  
Convex Metric Spaces

scholarly journals Strong Convergence Theorems for a Countable Family of Nonexpansive Mappings in Convex Metric Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-18 ◽  
Author(s):  
Withun Phuengrattana ◽  
Suthep Suantai
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Nonexpansive Mappings ◽  
Infinite Family ◽  
Convex Metric Space ◽  
Convergence Theorems ◽  
Convex Metric Spaces

We introduce a new modified Halpern iteration for a countable infinite family of nonexpansive mappings{Tn}in convex metric spaces. We prove that the sequence{xn}generated by the proposed iteration is an approximating fixed point sequence of a nonexpansive mapping when{Tn}satisfies the AKTT-condition, and strong convergence theorems of the proposed iteration to a common fixed point of a countable infinite family of nonexpansive mappings in CAT(0) spaces are established under AKTT-condition and the SZ-condition. We also generalize the concept ofW-mapping for a countable infinite family of nonexpansive mappings from a Banach space setting to a convex metric space and give some properties concerning the common fixed point set of this family in convex metric spaces. Moreover, by using the concept ofW-mappings, we give an example of a sequence of nonexpansive mappings defined on a convex metric space which satisfies the AKTT-condition. Our results generalize and refine many known results in the current literature.

Convergence theorems for generalized hemicontractive mapping in p-uniformly convex metric space

2020 ◽  
Vol 26 (2) ◽  
pp. 221-229
Author(s):  
Godwin C. Ugwunnadi ◽  
Chinedu Izuchukwu ◽  
Oluwatosin T. Mewomo
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Metric Spaces ◽  
Iteration Process ◽  
Uniformly Convex ◽  
Convex Metric Space ◽  
Convergence Theorems ◽  
Uniformly Convex Metric Space ◽  
Convex Metric Spaces ◽  
Hemicontractive Mappings

AbstractIn this paper, we introduce and study an Ishikawa-type iteration process for the class of generalized hemicontractive mappings in 𝑝-uniformly convex metric spaces, and prove both Δ-convergence and strong convergence theorems for approximating a fixed point of generalized hemicontractive mapping in complete 𝑝-uniformly convex metric spaces. We give a surprising example of this class of mapping that is not a hemicontractive mapping. Our results complement, extend and generalize numerous other recent results in CAT(0) spaces.

Convergence theorems for total asymptotically nonexpansive single-valued and quasi nonexpansive multi-valued mappings in hyperbolic spaces

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Preeyalak Chuadchawna ◽  
Ali Farajzadeh ◽  
Anchalee Kaewcharoen
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Hyperbolic Space ◽  
Hyperbolic Spaces ◽  
Iterative Sequence ◽  
Uniformly Convex ◽  
Convergence Theorems ◽  
Asymptotically Nonexpansive ◽  
Uniformly Convex Hyperbolic Space

Abstract In this paper, we discuss the Δ-convergence and strong convergence for the iterative sequence generated by the proposed scheme to approximate a common fixed point of a total asymptotically nonexpansive single-valued mapping and a quasi nonexpansive multi-valued mapping in a complete uniformly convex hyperbolic space. Finally, by giving an example, we illustrate our result.

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 Strong Convergence Theorems for a Common Fixed Point of a Family of Asymptoticallyk-Strict Pseudocontractive Mappings

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
H. Zegeye ◽  
N. Shahzad
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Banach Spaces ◽  
Iterative Process ◽  
Finite Family ◽  
Important Class ◽  
Convergence Theorems ◽  
Nonlinear Operators ◽  
Pseudocontractive Mappings

We provide an iterative process which converges strongly to a common fixed point of finite family of asymptoticallyk-strict pseudocontractive mappings in Banach spaces. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear operators.

scholarly journals Strong Convergence Theorems for Quasi-Bregman Nonexpansive Mappings in Reflexive Banach Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Mohammed Ali Alghamdi ◽  
Naseer Shahzad ◽  
Habtu Zegeye
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Banach Spaces ◽  
Nonexpansive Mappings ◽  
Maximal Monotone ◽  
Finite Family ◽  
Monotone Mappings ◽  
Reflexive Banach Spaces ◽  
Convergence Theorems

We study a strong convergence for a common fixed point of a finite family of quasi-Bregman nonexpansive mappings in the framework of real reflexive Banach spaces. As a consequence, convergence for a common fixed point of a finite family of Bergman relatively nonexpansive mappings is discussed. Furthermore, we apply our method to prove strong convergence theorems of iterative algorithms for finding a common solution of a finite family equilibrium problem and a common zero of a finite family of maximal monotone mappings. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear mappings.

Sign in / Sign up

Export Citation Format

Share Document