• 대한수학회보
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• 제47권2호
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• pp.295-305
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• 2010

In this paper, we show that the modified Mann iteration with errors converges strongly to fixed point for uniformly L-Lipschitzian asymptotically $\Phi$-pseudocontractive mappings in real Banach spaces. Meanwhile, it is proved that the convergence of Mann and Ishikawa iterations is equivalent for uniformly L-Lipschitzian asymptotically $\Phi$-pseudocontractive mappings in real Banach spaces. Finally, we obtain the convergence theorems of Ishikawa iterative sequence and the modified Ishikawa iterative process with errors.

• 대한수학회논문집
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• 제19권3호
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• pp.461-467
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• 2004

In this paper, we study the Ishikawa iterative sequences with errors for Lipschitzian strongly pseudo-contractive operator in arbitrary real Banach spaces. Our results improve the results obtained previously by C. E. Chidume [3] and Zeng [9].

• East Asian mathematical journal
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• 제25권1호
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• pp.27-37
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• 2009

In this paper, we introduce an iterative method for a pair of nonexpansive mappings. Strong convergence theorems are established in a real uniformly smooth Banach space.

• East Asian mathematical journal
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• 제17권2호
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• pp.265-273
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• 2001

In this paper, we prove that under certain conditions the Ishikawa iterative method with errors converges strongly to the unique solution of the nonlinear strongly accretive operator equation Tx=f. Related results deal with the solution of the equation x+Tx=f. Our results extend and improve the corresponding results of Liu, Childume, Childume-Osilike, Tan-Xu, Deng, Deng-Ding and others.

• 대한수학회보
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• 제44권4호
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• pp.861-870
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• 2007

In this paper, under suitable conditions, we show that the new class of iterative process with errors introduced by Li et al converges strongly to the unique solution of the equation involving strongly accretive operators in real Banach spaces. Furthermore, we prove that it is equivalent to the classical Ishikawa iterative sequence with errors.

• 대한수학회논문집
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• 제33권4호
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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.

• 대한수학회지
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• 제35권1호
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• pp.191-205
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• 1998

In this paper, we prove that the Mann and Ishikawa iteration sequences with errors converge strongly to the unique solution of the equation x + Tx = f, where T is an m-accretive operator in uniformly smooth Banach spaces. Our results extend and improve those of Chidume, Ding, Zhu and others.

• Nonlinear Functional Analysis and Applications
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• 제26권5호
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• pp.995-1009
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• 2021

Many iterative algorithms like that Picard, Mann, Ishikawa and S-iteration are very useful to elucidate the fixed point problems of a nonlinear operators in various topological spaces. The recent trend for elucidate the fixed point via inertial iterative algorithm, in which next iterative depends on more than one previous terms. The purpose of the paper is to establish convergence theorems of new inertial Picard normal S-iteration algorithm for nonexpansive mapping in Hilbert spaces. The comparison of convergence of InerNSP and InerPNSP is done with InerSP (introduced by Phon-on et al. [25]) and MSP (introduced by Suparatulatorn et al. [27]) via numerical example.

• Journal of applied mathematics & informatics
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• 제7권2호
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• pp.605-615
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• 2000

Let E be a real Banach space with property (U,${\lambda}$,m+1,m);${\lambda}{\ge}$0; m${\in}N$, and let C be a nonempty closed convex and bounded subset of E. Suppose T: $C{\leftrightarro}C$ is a strongly accretive map, It is proved that each of the two well known fixed point iteration methods( the Mann and Ishikawa iteration methods.), under suitable conditions , converges strongly to a solution of the equation Tx=f.

• Kyungpook Mathematical Journal
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• 제55권3호
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• pp.667-678
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• 2015

The aim of this paper is to prove strong convergence theorem by a modified three step iterative process with errors for three nonexpansive mappings in the frame work of uniformly smooth Banach spaces. The main feature of this scheme is that its special cases can handle both strong convergence like Halpern type and weak convergence like Ishikawa type iteration schemes. Our result extend and generalize the result of S. H. Khan, Kim and Xu and many other authors.