On minimization and fixed point problems in Hadamard spaces

In this paper, we incorporate proximal point algorithm with some convex combination techniques to approximate a minimizer and a common fixed point of a family of multi-valued mappings in Hadamard spaces. We prove -convergence and strong convergence theorems for a convex lower semi-continuous functio...

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Bibliographic Details
Published in:Computational & applied mathematics 2022-04, Vol.41 (3), Article 117
Main Authors: Salisu, Sani, Kumam, Poom, Sriwongsa, Songpon, Abubakar, Jamilu
Format: Article
Language:English
Subjects:
Algorithms
Applications of Mathematics
Applied physics
Computational mathematics
Computational Mathematics and Numerical Analysis
Continuity (mathematics)
Convergence
Fixed points (mathematics)
Hilbert space
Mathematical Applications in Computer Science
Mathematical Applications in the Physical Sciences
Mathematics
Mathematics and Statistics
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Summary:In this paper, we incorporate proximal point algorithm with some convex combination techniques to approximate a minimizer and a common fixed point of a family of multi-valued mappings in Hadamard spaces. We prove -convergence and strong convergence theorems for a convex lower semi-continuous function and multi-valued quasi-nonexpansive mappings. Furthermore, we apply our results to find mean, median and solve equilibrium problems in Hadamard spaces. Finally, we give two numerical examples, one in a non-Hilbert space with a non-convex functional and the other in a Hilbert space, to demonstrate the convergence of the proposed method.
ISSN:2238-3603
1807-0302
DOI:10.1007/s40314-022-01821-6