• Journal of applied mathematics & informatics
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• v.12 no.1_2
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• pp.119-127
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• 2003

The purpose of this paper is to study the necessary and sufficient conditions for the sequences of Ishikawa iterative sequences with mixed errors of asymptotically quasi-nonexpansive type mappings in Banach spaces to converge to a fixed point in Banach spaces. The results presented in this paper extend and improve the corresponding results of［l-4, 7-9].

• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.75-86
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• 2010

An iterative algorithm was been studied which can be viewed as an extension of the previously known algorithms for asymptotically nonexpansive mappings. Subsequently, we study the convergence problem of the proposed iterative algorithm for asymptotically nonexpansive mappings under some mild conditions in Banach spaces.

• East Asian mathematical journal
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• v.19 no.1
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• pp.103-111
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• 2003

In this paper, we will discuss some sufficient and necessary conditions for modified Ishikawa iterative sequence with mixed errors to converge to fixed points for asymptotically quasi-nonexpansive mappings in Banach spaces. The results presented in this paper extend, generalize and improve the corresponding results in Liu [4,5] and Ghosh-Debnath [2].

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.661-672
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• 2009

In this paper, we introduce a modified three-step iteration scheme with errors for asymptotically nonexpansive mappings in the framework of uniformly convex Banach spaces. Weak and strong convergence theorems are established.

• Communications of the Korean Mathematical Society
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• v.31 no.3
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• pp.483-493
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• 2016

In this paper, we study and prove common fixed point theorems for N generalized I-asymptotically nonexpansive mappings in a Hadamard space.

• The Pure and Applied Mathematics
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• v.20 no.1
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• pp.51-57
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• 2013

In this paper, we introduce asymptotically quasi-$f-g$-nonexpansive mappings in convex normed vector spaces and consider approximating common fixed points of a sequence of asymptotically quasi-$f-g$-nonexpansive mappings in convex normed vector spaces.

• Communications of the Korean Mathematical Society
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• v.29 no.1
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• pp.83-95
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• 2014

In a uniformly convex Banach space, we introduce a iterative scheme for a finite family of asymptotically quasi-nonexpansive mappings and utilize a new inequality to prove several convergence results for the iterative sequence. The results generalize and unify many important known results of relevant scholars.

• 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].

• Nonlinear Functional Analysis and Applications
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• v.27 no.4
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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.

• 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.