Ishikawa and Mann Iterative Processes with Errors for Nonlinear Strongly Accretive Operator Equations
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In this article, the convergence problem of Ishikawa and Mann iterative sequences for strongly pseudo-contractive mappings without the Lipschitz condition has been studied and the results presented in this paper improve and extend the corresponding results in [ 4, 5, 7, 10, 12, 15, 16 ] in the more general setting.About:
This article is published in Journal of Mathematical Analysis and Applications.The article was published on 1998-08-01 and is currently open access. It has received 250 citations till now. The article focuses on the topics: Lipschitz continuity & Operator (computer programming).read more
Citations
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Journal ArticleDOI
Weak and strong convergence theorems for three-step iterations with errors for asymptotically nonexpansive mappings☆
TL;DR: In this article, several weak and strong convergence theorems are established for the three-step iterative schemes with errors for asymptotically nonexpansive mappings.
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Weak and strong convergence theorems for fixed points of asymptotically nonexpensive mappings
M.O. Osilike,S. C. Aniagbosor +1 more
TL;DR: Weak and strong convergence theorems for the iterative approximation of fixed points of T are proved in this paper, where the boundedness requirement imposed on the subset K in recent results of Huang [1], Rhoades [2], and Schu [3,4] can be dropped.
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Weak and strong convergence of a scheme with errors for two nonexpansive mappings
TL;DR: In this article, a weak and strong convergence of an iterative scheme in a uniformly convex Banach space under a condition weaker than compactness was studied. But the convergence of the scheme was not considered.
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Convergence of iterates with errors of asymptotically quasi-nonexpansive mappings and applications
TL;DR: In this article, a generalized iterative process with errors is considered to approximate the common fixed points of two asymptotically quasi-none-expansive mappings, and a convergence theorem has been obtained which generalizes a known result.
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Weak and strong convergence theorems for fixed points of pseudocontractions and solutions of monotone type operator equations
M.O. Osilike,D.I. Igbokwe +1 more
TL;DR: Weak and strong convergence theorems for the iterative approximation of fixed points of a Lipschitz monotone operator were proved in this article, where Tx = f is a nonempty fixed point set.
References
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Book
Nonlinear Functional Analysis
TL;DR: A survey of the main ideas, concepts, and methods that constitute nonlinear functional analysis can be found in this article, with extensive commentary, many examples, and interesting, challenging exercises.
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Mean value methods in iteration
TL;DR: In this article, it is shown that the Schauder fixpoint theorem can play a somewhat analogous role in the theory of divergent iteration processes, and that the same methods can be used to prove that a given problem has a solution.
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