• Communications of the Korean Mathematical Society
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• v.31 no.3
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• pp.507-518
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• 2016

The aim of this paper is to prove some strong convergence theorems for the modified Ishikawa iteration process involving a pair of a generalized asymptotically nonexpansive single-valued mapping and a quasi-nonexpansive multi-valued mapping in the framework of $\mathbb{R}$-trees under the gate condition.

• East Asian mathematical journal
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• v.28 no.5
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• pp.617-630
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• 2012

In this paper, the problem of iterative approximation of common fixed points of asymptotically nonexpansive is investigated in the framework of Banach spaces. Weak convergence theorems are established. A necessary and sufficient condition for strong convergence is also discussed. As an application of main results, a variational inequality is investigated.

• Kyungpook Mathematical Journal
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• v.48 no.1
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• pp.133-142
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• 2008

In this paper, we prove two strong convergence theorems for asymptotically nonexpansive mappings in Hibert spaces by hybrid methods. Our results extend and improve the recent ones announced by Nakajo, Takahashi [K. Nakajo, W. Takahashi, Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups, J. Math. Anal. Appl. 279 (2003) 372-379], Kim, 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], Martinez-Yanes, Xu [C. Martinez-Yanes, H. K. Xu, Strong convergence of the CQ method for fixed point iteration processes, Nonlinear Anal. 64 (2006) 2400-2411] and some others.

• Communications of the Korean Mathematical Society
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• v.27 no.1
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• pp.167-174
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• 2012

In this paper, we introduce an asymptotically $\phi$-hemicontractive mapping with a $\phi$-normalized duality mapping and obtain some strongly convergent result of a kind of multi-step iteration schemes for asymptotically $\phi$-hemicontractive mappings.

• Kyungpook Mathematical Journal
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• v.59 no.4
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• pp.665-678
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• 2019

We construct an iteration scheme involving a hybrid pair of mappings, one a single-valued asymptotically nonexpansive mapping t and the other a multivalued nonexpansive mapping T, in a complete CAT(0) space. In the process, we remove a restricted condition (called the end-point condition) from results of Akkasriworn and Sokhuma [1] and and use this to prove some convergence theorems. The results concur with analogues for Banach spaces from Uddin et al. [16].

• Communications of the Korean Mathematical Society
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• v.15 no.2
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• pp.275-284
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• 2000

The existence and convergence theorems for fixed points of mappings of asymptotically nonexpansive type are established in Banach spaces with a weakly continuous duality mapping but without uniform convexity.

• Communications of the Korean Mathematical Society
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• v.30 no.3
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• pp.177-189
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• 2015

In this paper, we prove ${\Delta}$-convergence theorems for Ishikawa iteration of asymptotically and multivalued nonexpansive mapping in CAT(0) spaces. This results we obtain are analogs of Banach spaces results of Sokhuma [13].

• Bulletin of the Korean Mathematical Society
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• v.38 no.3
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• pp.611-622
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• 2001

Some convergence theorems of modified Ishikawa and Mann iteration processes with errors for asymptotically pseudo-contractive and asymptotically nonexpansive mappings in Banach spaces are obtained. The results presented in this paper improve and extend the corresponding results in Liu [7] and Schu [10].

• 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].

• Kyungpook Mathematical Journal
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• v.63 no.3
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• pp.451-461
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• 2023

In this paper, we study the fixed point property for generalized asymptotically nonexpansive mappings in the setting of p-Hadamard spaces, with p ≥ 2. We prove the strong convergence of the sequence generated by the modified two-step iterative sequence for finding a fixed point of a generalized asymptotically nonexpansive mapping in p-Hadamard spaces.