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Research Article | Open Access

On a proximal point algorithm for solving common fixed point problems and convex minimization problems in Geodesic spaces with positive curvature

Chainarong Khunpanuk1, Chanchal Garodia2, Izhar Uddin2, Nuttapol Pakkaranang1( )
Mathematics and Computing Science Program, Faculty of Science and Technology, Phetchabun Rajabhat University, Phetchabun 67000, Thailand
Department of Mathematics, Faculty of Natural Sciences, Jamia Millia Islamia, New Delhi-110025, India
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Abstract

In this article, we present a new modified proximal point algorithm in the framework of CAT(1) spaces which is utilized for solving common fixed point problem and minimization problems. Also, we prove convergence results of the obtained process under some mild conditions. Our results extend and improve several corresponding results of the existing literature.

Keywords

minimization problemresolvent operatorCAT(1) spaceproximal point algorithmnonexpansive mapping
CLC number: 47H09, 47H10, 47J05, 52A41

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AIMS Mathematics
Volume 7 Issue 5,
May 2022
Pages 9509-9523
DOI: 10.3934/math.2022529

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Cite this article:
Khunpanuk C, Garodia C, Uddin I, et al. On a proximal point algorithm for solving common fixed point problems and convex minimization problems in Geodesic spaces with positive curvature. AIMS Mathematics, 2022, 7(5): 9509-9523. https://doi.org/10.3934/math.2022529

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Received: 06 September 2021
Revised: 20 February 2022
Accepted: 06 March 2022
Published: 15 May 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)