The Implicit Midpoint Procedures for Asymptotically Nonexpansive Mappings

The concept of asymptotically nonexpansive mappings is an important generalization of the class of nonexpansive mappings. Implicit midpoint procedures are extremely fundamental for solving equations involving nonlinear operators. This paper studies the convergence analysis of the class of asymptotic...

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Bibliographic Details
Main Authors: M. O. Aibinu, S. C. Thakur, S. Moyo
Format: Article
Language:English
Published: Wiley 2020-01-01
Series:Journal of Mathematics
Online Access:http://dx.doi.org/10.1155/2020/6876385
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Summary:The concept of asymptotically nonexpansive mappings is an important generalization of the class of nonexpansive mappings. Implicit midpoint procedures are extremely fundamental for solving equations involving nonlinear operators. This paper studies the convergence analysis of the class of asymptotically nonexpansive mappings by the implicit midpoint iterative procedures. The necessary conditions for the convergence of the class of asymptotically nonexpansive mappings are established, by using a well-known iterative algorithm which plays important roles in the computation of fixed points of nonlinear mappings. A numerical example is presented to illustrate the convergence result. Under relaxed conditions on the parameters, some algorithms and strong convergence results were derived to obtain some results in the literature as corollaries.
ISSN:2314-4629
2314-4785