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http://dx.doi.org/10.22771/nfaa.2021.26.04.02

ON GENERALIZED (𝛼, 𝛽)-NONEXPANSIVE MAPPINGS IN BANACH SPACES WITH APPLICATIONS  

Akutsah, F. (School of Mathematics, Statistics and Computer Science University of KwaZulu-Natal)
Narain, O.K. (School of Mathematics, Statistics and Computer Science University of KwaZulu-Natal)
Publication Information
Nonlinear Functional Analysis and Applications / v.26, no.4, 2021 , pp. 663-684 More about this Journal
Abstract
In this paper, we present some fixed point results for a general class of nonexpansive mappings in the framework of Banach space and also proposed a new iterative scheme for approximating the fixed point of this class of mappings in the frame work of uniformly convex Banach spaces. Furthermore, we establish some basic properties and convergence results for our new class of mappings in uniformly convex Banach spaces. Finally, we present an application to nonlinear integral equation and also, a numerical example to illustrate our main result and then display the efficiency of the proposed algorithm compared to different iterative algorithms in the literature with different choices of parameters and initial guesses. The results obtained in this paper improve, extend and unify some related results in the literature.
Keywords
Generalized (${\alpha},\; {\beta}$)-nonexpansive type 1 mapping; generalized (${\alpha},\; {\beta}$)-nonexpansive type 2 mapping; fixed point; iterative scheme; strong and weak convergence theorems;
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