Convergence of Implicit Iteration Process for a Finite Family of Asymptotically Nonexpansive Mappings in Banach Spaces

Zhou, Yuying; Chang, Shih-sen

doi:10.1081/nfa-120016276

Cited by 68 publications

(50 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The results presented in this paper not only generalized and extend the corresponding results in [1], [2], [4]- [9], [11]- [15], but also give an affirmative to the open question suggested by Xu and Ori [14]. Moreover the results even in the case of u n = v n = 0 or β n = 0, v n = 0, ∀n ≥ 1 are also new.…”

Section: Introductionsupporting

confidence: 84%

“…Recently, concerning the convergence problems of an implicit (or nonimplicit) iterative process to a common fixed point for a finite family of asymptotically nonexpansive mappings (or nonexpansive mappings) in Hilbert spaces or uniformly convex Banach spaces have been considered by several authors (see, for example, Bauschke [1], Chang and Cho [2], Goebel and Kirk [4], Górnicki [5], Halpern [6], Lions [7], Osilike [8], Reich [9], Schu [10], Sun [11], Tan and Xu [12], Wittmann [13], Xu and Ori [14] and Zhou and Chang [15]). …”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Strong and Weak Convergence of Implicit Iterative Process with Errors for Asymptotically Nonexpansive Mappings

Gu¹

2006

Journal of Applied Analysis

View full text Add to dashboard Cite

show abstract

Section: Introductionsupporting

confidence: 84%

Section: Introductionmentioning

confidence: 99%

Strong and Weak Convergence of Implicit Iterative Process with Errors for Asymptotically Nonexpansive Mappings

Gu¹

2006

Journal of Applied Analysis

View full text Add to dashboard Cite

show abstract

“…Xu and Ori [10] proved the weak convergence of an implicit iterative process to a common fixed point of the finite family of nonexpansive mappings defined in Hilbert space. Zhou and Chang [11], in 2002, studied the weak and strong convergence of implicit iteration process to a common fixed point for a finite family of nonexpansive mappings in Banach spaces. Chidume-Shahzad [2], in 2005, proved the strong convergence of an implicit iteration process to a common fixed point for a finite family of nonexpansive mappings in Banach spaces.…”

Section: S Temirmentioning

confidence: 99%

Convergence of an implicit iteration process with errors for two asymptotically nonexpansive mappings

Temir

2013

Demonstratio Mathematica

View full text Add to dashboard Cite

Abstract. The purpose of this paper is to introduce an implicit iterative process with errors for approximating common fixed point of two finite families of asymptotically nonexpansive mappings in the framework of Banach space. The results presented in this paper extend and generalize the corresponding results of Qin et al. IntroductionLet K be a nonempty subset of a real Banach space X and T : K → K be a mapping. Let F (T ) = {x ∈ K : T x = x} be denoted as the set of fixed points of T .A mapping T : K → K is called nonexpansive providedfor all x, y ∈ K and n ≥ 1. An important generalization of the class of nonexpansive mappings and the class of asymptotically nonexpansive mappings was introduced by Goebel and Kirk [4]. They proved that every asymptotically nonexpansive selfmapping of a nonempty closed convex subset of a uniformly convex Banach space has a fixed point.T is called asymptotically nonexpansive mapping if there exists a sequence {k n } ⊂ [1, ∞) with lim n→∞ k n = 1 such thatfor all x, y ∈ K and n ≥ 1. A mapping T : K → K is called uniformly 2010 Mathematics Subject Classification: 47H09; 47H10.

show abstract

“…This process proved to be the main tool to approximate common fixed points of various class of mappings in deterministic operator theory. Zhao and Chang [31] studied convergence of the modified implicit iteration process to common fixed point of a finite family of asymptotically nonexpansive mappings. Sun [26] proved necessary and sufficient conditions for convergence of an implicit iteration process to a common fixed point of asymptotically quasi-nonexpansive mappings.…”

Section: Introductionmentioning

confidence: 99%

Implicit random iteration process with errors for asymptotically quasi-nonexpansive in the intermediate sense random operators

Saluja¹

2012

OpMath

View full text Add to dashboard Cite

Abstract. In this paper, we give a necessary and sufficient condition for the strong convergence of an implicit random iteration process with errors to a common fixed point for a finite family of asymptotically quasi-nonexpansive in the intermediate sense random operators and also prove some strong convergence theorems using condition (C) and the semi-compact condition for said iteration scheme and operators. The results presented in this paper extend and improve the recent ones obtained by S. Plubtieng, P. Kumam and R. Wangkeeree, and also by the author.Keywords: asymptotically quasi-nonexpansive in the intermediate sense random operator, implicit random iteration process with errors, common random fixed point, strong convergence, separable uniformly convex Banach space.Mathematics Subject Classification: 47H10, 47J25.

show abstract

Convergence of Implicit Iteration Process for a Finite Family of Asymptotically Nonexpansive Mappings in Banach Spaces

Cited by 68 publications

References 8 publications

Strong and Weak Convergence of Implicit Iterative Process with Errors for Asymptotically Nonexpansive Mappings

Strong and Weak Convergence of Implicit Iterative Process with Errors for Asymptotically Nonexpansive Mappings

Convergence of an implicit iteration process with errors for two asymptotically nonexpansive mappings

Implicit random iteration process with errors for asymptotically quasi-nonexpansive in the intermediate sense random operators

Contact Info

Product

Resources

About