A modified proximal point algorithm in geodesic metric space

Chanchal Garodia; Izhar Uddin; Bahaaeldin Abdalla; Thabet Abdeljawad; Chanchal Garodia; Izhar Uddin; Bahaaeldin Abdalla; Thabet Abdeljawad

doi:10.3934/math.2023214

AIMS Mathematics

2023, Volume 8, Issue 2: 4304-4320. doi: 10.3934/math.2023214

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Research article

A modified proximal point algorithm in geodesic metric space

1.
Department of Mathematics, Faculty of Natural Sciences, Jamia Millia Islamia, New Delhi-110025, India
2.
Department of Mathematics and Sciences, Prince Sultan University, P.O. Box 66833, Riyadh 11586, Saudi Arabia
3.
Department of Medical Research, China Medical University, Taichung 40402, Taiwan

Received: 27 July 2022 Revised: 18 November 2022 Accepted: 23 November 2022 Published: 05 December 2022
MSC : 47H09, 47H10

Proximal point algorithm is one of the most popular technique to find either zero of monotone operator or minimizer of a lower semi-continuous function. In this paper, we propose a new modified proximal point algorithm for solving minimization problems and common fixed point problems in CAT(0) spaces. We prove $ \Delta $ and strong convergence of the proposed algorithm. Our results extend and improve the corresponding recent results in the literature.
- minimization problem,
- resolvent operator,
- CAT$ (0) $ space,
- proximal point algorithm,
- nonexpansive mappings
Citation: Chanchal Garodia, Izhar Uddin, Bahaaeldin Abdalla, Thabet Abdeljawad. A modified proximal point algorithm in geodesic metric space[J]. AIMS Mathematics, 2023, 8(2): 4304-4320. doi: 10.3934/math.2023214

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Abstract

Proximal point algorithm is one of the most popular technique to find either zero of monotone operator or minimizer of a lower semi-continuous function. In this paper, we propose a new modified proximal point algorithm for solving minimization problems and common fixed point problems in CAT(0) spaces. We prove $ \Delta $ and strong convergence of the proposed algorithm. Our results extend and improve the corresponding recent results in the literature.

References

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