Approximation of Fixed Points of Multivalued Generalized ( ?, ? )-Nonexpansive Mappings in an Ordered CAT(0) Space

Mujahid Abbas, Hira Iqbal, Manuel De la Sen and Khushdil Ahmad
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Mujahid Abbas: Department of Mathematics, Government College University, Katchery Road, Lahore 54000, Pakistan
Hira Iqbal: Department of Sciences and Humanities, Lahore Campus, National University of Computer and Emerging Sciences, Lahore 54000, Pakistan
Manuel De la Sen: Institute of Research and Development of Processes, University of the Basque Country, 48940 Leioa, Spain
Khushdil Ahmad: Department of Mathematics, Government College University, Katchery Road, Lahore 54000, Pakistan

Mathematics, 2021, vol. 9, issue 16, 1-21

Abstract: The purpose of this article is to initiate the notion of monotone multivalued generalized ( ? , ? )-nonexpansive mappings and explore the iterative approximation of the fixed points for the mapping in an ordered CAT(0) space. In particular, we employ the S -iteration algorithm in CAT(0) space to prove some convergence results. Moreover, some examples and useful results related to the proposed mapping are provided. Numerical experiments are also provided to illustrate and compare the convergence of the iteration scheme. Finally, an application of the iterative scheme has been presented in finding the solutions of integral differential equation.

Keywords: multivalued nonexpansive mapping; fixed point; monotone; CAT(0) space (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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