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Volume 9
Issue 16
10.3390/math9161945
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Article

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

by
Mujahid Abbas
1,2,
Hira Iqbal
3,
Manuel De la Sen
4,* and
Khushdil Ahmad
1
1
Department of Mathematics, Government College University, Katchery Road, Lahore 54000, Pakistan
2
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 404, Taiwan
3
Department of Sciences and Humanities, Lahore Campus, National University of Computer and Emerging Sciences, Lahore 54000, Pakistan
4
Institute of Research and Development of Processes, University of the Basque Country, 48940 Leioa, Spain
*
Author to whom correspondence should be addressed.
Mathematics 2021, 9(16), 1945; https://doi.org/10.3390/math9161945
Submission received: 7 July 2021 / Revised: 9 August 2021 / Accepted: 10 August 2021 / Published: 15 August 2021
(This article belongs to the Special Issue Nonlinear Problems and Applications of Fixed Point Theory)
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Abstract

The purpose of this article is to initiate the notion of monotone multivalued generalized (α,β)-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 multivalued nonexpansive mapping; fixed point; monotone; CAT(0) space

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MDPI and ACS Style

Abbas, M.; Iqbal, H.; De la Sen, M.; Ahmad, K. Approximation of Fixed Points of Multivalued Generalized (α,β)-Nonexpansive Mappings in an Ordered CAT(0) Space. Mathematics 2021, 9, 1945. https://doi.org/10.3390/math9161945

AMA Style

Abbas M, Iqbal H, De la Sen M, Ahmad K. Approximation of Fixed Points of Multivalued Generalized (α,β)-Nonexpansive Mappings in an Ordered CAT(0) Space. Mathematics. 2021; 9(16):1945. https://doi.org/10.3390/math9161945

Chicago/Turabian Style

Abbas, Mujahid, Hira Iqbal, Manuel De la Sen, and Khushdil Ahmad. 2021. "Approximation of Fixed Points of Multivalued Generalized (α,β)-Nonexpansive Mappings in an Ordered CAT(0) Space" Mathematics 9, no. 16: 1945. https://doi.org/10.3390/math9161945

APA Style

Abbas, M., Iqbal, H., De la Sen, M., & Ahmad, K. (2021). Approximation of Fixed Points of Multivalued Generalized (α,β)-Nonexpansive Mappings in an Ordered CAT(0) Space. Mathematics, 9(16), 1945. https://doi.org/10.3390/math9161945

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