• Journal of applied mathematics & informatics
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• 제28권1_2호
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• pp.87-98
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• 2010

The purpose of this paper is to prove a weak convergence theorem for a common fixed points of finite family of nonspreading mappings and nonexpansive mappings in Hilbert spaces. The results presented in this paper extend and improve the results of Mondafi [A. Moudafi, Krasnoselski-Mann iteration for hierarchical fixed-point problems, Inverse Problems 23 (2007) 1635-1640], and Iemoto and Takahashi [So Iemoto, W.Takahashi, Approximating common fixed points of nonexpansive mappings and nonspreading mappings in a Hilbert space, Nonlinear Analysis (2009), doi:10.1016/j.na.2009.03.064].

• 대한수학회지
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• 제38권6호
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• pp.1275-1284
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• 2001

In this paper, we introduce an iteration generated by countable nonexpansive mappings and prove a weak convergence theorem which is connected with the feasibility problem. This result is used to solve the problem of finding a solution of the countable convex inequality system and the problem of finding a common fixed point for a commuting countable family of nonexpansive mappings.

• 충청수학회지
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• 제21권3호
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• pp.327-337
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• 2008

In this paper, we prove strong convergence theorems of Halpern iteration for relatively asymptotically nonexpansive mappings in the framework of Banach spaces. Our results extend and improve the recent ones announced by [C. Martinez-Yanes, H. K. Xu, Strong convergence of the CQ method for fixed point iteration processes, Nonlinear Anal. 64 (2006), 2400-2411], [X. Qin, Y. Su, Strong convergence theorem for relatively nonexpansive mappings in a Banach space, Nonlinear Anal. 67 (2007), 1958-1965] and many others.

• Korean Journal of Mathematics
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• 제18권3호
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• pp.213-227
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• 2010

Convergence of an implicit iterative process is investigated for nonexpansive mappings. Strong and weak convergence theorems of common fixed points of two finite families of nonexpansive mappings are established in the framework of Banach spaces.

• 대한수학회논문집
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• 제26권1호
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• pp.51-65
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• 2011

In this paper, a composite iterative process is introduced for a generalized equilibrium problem and a pair of nonexpansive mappings. It is proved that the sequence generated in the purposed composite iterative process converges strongly to a common element of the solution set of a generalized equilibrium problem and of the common xed point of a pair of nonexpansive mappings.

• Journal of applied mathematics & informatics
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• 제30권1_2호
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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].

• East Asian mathematical journal
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• 제26권3호
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• pp.337-350
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• 2010

Strong convergence theorem of the explicit viscosity iterative scheme involving the sunny nonexpansive retraction for nonexpansive nonself-mappings is established in a reflexive and strictly convex Banach spaces having a weakly sequentially continuous duality mapping. The main result improves the corresponding result of [19] to the more general class of mappings together with certain different control conditions.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제16권1호
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• pp.85-98
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• 2009

Strong convergence theorems on viscosity approximation methods for finite nonexpansive mappings are established in Banach spaces. The main theorem generalize the corresponding result of Kim and Xu [10] to the viscosity approximation method for finite nonexpansive mappings in a reflexive Banach space having a uniformly Gateaux differentiable norm. Our results also improve the corresponding results of [7, 8, 19, 20].

• Kyungpook Mathematical Journal
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• 제48권4호
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• pp.685-703
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• 2008

Motivated and inspired by ideas due to Matsushida and Takahashi [J. Approx. Theory 134(2005), 257-266] and Martinez-Yanes and Xu [Nonlinear Anal. 64(2006), 2400-2411], we prove some strong convergence theorems of modified iteration processes for a pair (or finite family) of relatively nonexpansive mappings in Banach spaces, which improve and extend the corresponding results of Matsushida and Takahashi and Martinez-Yanes and Xu in Banach and Hilbert spaces, repectively.

• Nonlinear Functional Analysis and Applications
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• 제27권4호
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• pp.903-920
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• 2022

In this paper, we propose and study an implicit iteration process for a finite family of total asymptotically quasi-nonexpansive mappings and a finite family of asymptotically quasi-nonexpansive mappings in the intermediate sense in convex metric spaces and establish some strong convergence results. Also, we give some applications of our result in the setting of convex metric spaces. The results of this paper are generalizations, extensions and improvements of several corresponding results.