• Title, Summary, Keyword: asymptotically S-nonexpansive mapping

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HYBRID MONOTONE PROJECTION ALGORITHMS FOR ASYMPTOTICALLY QUASI-PSEUDOCONTRACTIVE MAPPINGS

  • Wu, Changqun;Cho, Sun-Young
    • East Asian mathematical journal
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    • v.25 no.4
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    • pp.415-423
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    • 2009
  • In this paper, we consider the hybrid monotone projection algorithm for asymptotically quasi-pseudocontractive mappings. A strong convergence theorem is established in the framework of Hilbert spaces. Our results mainly improve the corresponding results announced by [H. Zhou, Demiclosedness principle with applications for asymptotically pseudo-contractions in Hilbert spaces, Nonlinear Anal. 70 (2009) 3140-3145] and also include Kim and Xu [T.H. Kim, H.K. Xu, Strong convergence of modified Mann iterations for asymptotically nonexpansive mappings and semigroups, Nonlinear Anal. 64 (2006) 1140-1152; Convergence of the modified Mann's iteration method for asymptotically strict pseudo-contractions, Nonlinear Anal. 68 (2008) 2828-2836] as special cases.

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APPROXIMATING COMMON FIXED POINTS FOR TOTAL ASYMPTOTICALLY NONEXPANSIVE MAPPINGS

  • Kim, Gang-Eun
    • Journal of applied mathematics & informatics
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    • v.30 no.1_2
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    • pp.71-82
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    • 2012
  • In this paper, we first show the weak convergence of the modified Ishikawa iteration process with errors of two total asymptotically nonexpansive mappings, which generalizes the result due to Khan and Fukhar-ud-din [1]. Next, we show the strong convergence of the modified Ishikawa iteration process with errors of two total asymptotically nonexpansive mappings satisfying Condition ($\mathbf{A}^{\prime}$), which generalizes the result due to Fukhar-ud-din and Khan [2].

STRONG CONVERGENCE OF MODIFIED ISHIKAWA ITERATES FOR ASYMPTOTICALLY NONEXPANSIVE MAPS WITH NEW CONTROL CONDITIONS

  • Eldred, A. Anthony;Mary, P. Julia
    • Communications of the Korean Mathematical Society
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    • v.33 no.4
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    • pp.1271-1284
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    • 2018
  • In this paper, we establish strong convergence of the modified Ishikawa iterates of an asymptotically non expansive self-mapping of a nonempty closed bounded and convex subset of a uniformly convex Banach space under a variety of new control conditions.

CONVERGENCE TO COMMON FIXED POINTS FOR A FINITE FAMILY OF GENERALIZED ASYMPTOTICALLY QUASI-NONEXPANSIVE MAPPINGS IN BANACH SPACES

  • Saluja, G.S.
    • East Asian mathematical journal
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    • v.29 no.1
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    • pp.23-37
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    • 2013
  • The purpose of this paper is to study an implicit iteration process with errors and establish weak and strong convergence theorems to converge to common fixed points for a finite family of generalized asymptotically quasi-nonexpansive mappings in the framework of uniformly convex Banach spaces. Our results extend, improve and generalize some known results from the existing literature.

AN IMPLICIT ITERATES FOR NON-LIPSCHITZIAN ASYMPTOTICALLY QUASI-NONEXPANSIVE TYPE MAPPINGS IN CAT(0) SPACES

  • Saluja, G.S.
    • East Asian mathematical journal
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    • v.28 no.1
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    • pp.81-92
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    • 2012
  • The purpose of this paper is to establish strong convergence of an implicit iteration process to a common fixed point for a finite family of asymptotically quasi-nonexpansive type mappings in CAT(0) spaces. Our results improve and extend the corresponding results of Fukhar-ud-din et al. [15] and some others from the current literature.

Approximating Common Fixed Points of One-step Iterative Scheme with Error for Asymptotically Quasi-nonexpansive Type Nonself-Mappings

  • Puturong, Narongrit
    • Kyungpook Mathematical Journal
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    • v.49 no.4
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    • pp.667-674
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    • 2009
  • In this paper, a new one-step iterative scheme with error for approximating common fixed points of asymptotically quasi-nonexpansive type nonself-mappings in Banach space is defined. The results obtained in this paper extend and improve the recent ones, announced by H. Y. Zhou, Y. J. Cho, and S. M. Kang [Zhou et al.,(2007), namely, A new iterative algorithm for approximating common fixed points for asymptotically non-expansive mappings, published to Fixed Point Theory and Applications 2007 : 1-9], and many others.

STRONG CONVERGENCE OF HYBRID ITERATIVE SCHEMES WITH ERRORS FOR EQUILIBRIUM PROBLEMS AND FIXED POINT PROBLEMS

  • Kim, Seung-Hyun;Kang, Mee-Kwang
    • The Pure and Applied Mathematics
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    • v.25 no.2
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    • pp.149-160
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    • 2018
  • In this paper, we prove a strong convergence result under an iterative scheme for N finite asymptotically $k_i-strictly$ pseudo-contractive mappings and a firmly nonexpansive mappings $S_r$. Then, we modify this algorithm to obtain a strong convergence result by hybrid methods. Our results extend and unify the corresponding ones in [1, 2, 3, 8]. In particular, some necessary and sufficient conditions for strong convergence under Algorithm 1.1 are obtained.

CONVERGENCE THEOREMS OF IMPLICIT ITERATION PROCESS WITH ERRORS FOR ASYMPTOTICALLY NONEXPANSIVE MAPPINGS IN THE INTERMEDIATE SENSE IN BANACH SPACES

  • Saluja, G.S.
    • East Asian mathematical journal
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    • v.28 no.1
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    • pp.63-71
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    • 2012
  • The aim of this article is to study an implicit iteration process with errors for a finite family of non-Lipschitzian asymptotically non expansive mappings in the intermediate sense in Banach spaces. Also we establish some strong convergence theorems and a weak convergence theorem for said scheme to converge to a common fixed point for non Lipschitzian asymptotically nonexpansive mappings in the intermediate sense. The results presented in this paper extend and improve the corresponding results of [1], [3]-[8], [10]-[11], [13]-[14], [16] and many others.