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

Chainarong Khunpanuk; Chanchal Garodia; Izhar Uddin; Nuttapol Pakkaranang; Chainarong Khunpanuk; Chanchal Garodia; Izhar Uddin; Nuttapol Pakkaranang

doi:10.3934/math.2022529

AIMS Mathematics

2022, Volume 7, Issue 5: 9509-9523. doi: 10.3934/math.2022529

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Research article

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

1.
Mathematics and Computing Science Program, Faculty of Science and Technology, Phetchabun Rajabhat University, Phetchabun 67000, Thailand
2.
Department of Mathematics, Faculty of Natural Sciences, Jamia Millia Islamia, New Delhi-110025, India

Received: 06 September 2021 Revised: 20 February 2022 Accepted: 06 March 2022 Published: 14 March 2022
MSC : 47H09, 47H10, 47J05, 52A41

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.
- minimization problem,
- resolvent operator,
- CAT(1) space,
- proximal point algorithm,
- nonexpansive mapping
Citation: Chainarong Khunpanuk, Chanchal Garodia, Izhar Uddin, Nuttapol Pakkaranang. On a proximal point algorithm for solving common fixed point problems and convex minimization problems in Geodesic spaces with positive curvature[J]. AIMS Mathematics, 2022, 7(5): 9509-9523. doi: 10.3934/math.2022529

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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.

References

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