International Journal of Nonlinear Analysis and Applications
Convergence analysis and approximation of fixed point of multivalued generalized $\alpha$-nonexpansive mapping in uniformly convex Banach space
Document Type : Research Paper
Authors
Department of Mathematics, Michael Okpara University of Agriculture, Umudike, Abia State, Nigeria
Abstract
Recently, the authors introduce a four-step iterative algorithm called the UD-iteration scheme (Udofia and Igbokwe [35]). Here we introduce the multivalued version of the UD-iteration scheme and show that it can be used to approximate the fixed points of multivalued contraction and multivalued generalized $\alpha$-nonexpansive mappings. we prove strong and weak convergence of the iteration scheme to the fixed point of multivalued generalized $\alpha$-nonexpansive mapping. We also prove that the scheme is $\varUpsilon$-stable and Data dependent. Convergence analysis shows that the multivalued UD-iteration scheme has a faster rate of convergence for multivalued contraction and multivalued generalized $\alpha$-nonexpansive mappings than some well-known existing iteration schemes in the literature.
Keywords
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Volume 14, Issue 2
February 2023Pages 45-74
- Receive Date: 13 July 2022
- Revise Date: 18 August 2022
- Accept Date: 24 August 2022