Triple Mann Iteration Method for Variational Inclusions, Equilibria, and Common Fixed Points of Finitely Many Quasi-Nonexpansive Mappings on Hadamard Manifolds

Ceng, Lu-Chuan; Huang, Yun-Yi; Li, Si-Ying; Yao, Jen-Chih

doi:10.3390/math13030444

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Triple Mann Iteration Method for Variational Inclusions, Equilibria, and Common Fixed Points of Finitely Many Quasi-Nonexpansive Mappings on Hadamard Manifolds

¹

Department of Mathematics, Shanghai Normal University, Shanghai 200234, China

²

Research Center for Interneural Computing, China Medical University Hospital, China Medical University, Taichung 404327, Taiwan

³

Academy of Romanian Scientists, 50044 Bucharest, Romania

^*

Author to whom correspondence should be addressed.

Mathematics 2025, 13(3), 444; https://doi.org/10.3390/math13030444

Submission received: 14 January 2025 / Revised: 23 January 2025 / Accepted: 25 January 2025 / Published: 28 January 2025

(This article belongs to the Special Issue Current Topics in Optimization, Inequalities and Convex Function Theory)

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Abstract

In this paper, we introduce a triple Mann iteration method for approximating an element in the set of common solutions of a system of quasivariational inclusion issues, which is an equilibrium problem and a common fixed point problem (CFPP) of finitely many quasi-nonexpansive operators on a Hadamard manifold. Through some suitable assumptions, we prove that the sequence constructed in the suggested algorithm is convergent to an element in the set of common solutions. Finally, making use of the main result, we deal with the minimizing problem with a CFPP constraint and saddle point problem with a CFPP constraint on a Hadamard manifold, respectively.

Keywords: triple Mann iteration method; quasivariational inclusion issue; equilibrium problem; maximal monotone vector field; quasi-nonexpansive mapping; Hadamard’s manifold

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MDPI and ACS Style

Ceng, L.-C.; Huang, Y.-Y.; Li, S.-Y.; Yao, J.-C. Triple Mann Iteration Method for Variational Inclusions, Equilibria, and Common Fixed Points of Finitely Many Quasi-Nonexpansive Mappings on Hadamard Manifolds. Mathematics 2025, 13, 444. https://doi.org/10.3390/math13030444

AMA Style

Ceng L-C, Huang Y-Y, Li S-Y, Yao J-C. Triple Mann Iteration Method for Variational Inclusions, Equilibria, and Common Fixed Points of Finitely Many Quasi-Nonexpansive Mappings on Hadamard Manifolds. Mathematics. 2025; 13(3):444. https://doi.org/10.3390/math13030444

Chicago/Turabian Style

Ceng, Lu-Chuan, Yun-Yi Huang, Si-Ying Li, and Jen-Chih Yao. 2025. "Triple Mann Iteration Method for Variational Inclusions, Equilibria, and Common Fixed Points of Finitely Many Quasi-Nonexpansive Mappings on Hadamard Manifolds" Mathematics 13, no. 3: 444. https://doi.org/10.3390/math13030444

APA Style

Ceng, L.-C., Huang, Y.-Y., Li, S.-Y., & Yao, J.-C. (2025). Triple Mann Iteration Method for Variational Inclusions, Equilibria, and Common Fixed Points of Finitely Many Quasi-Nonexpansive Mappings on Hadamard Manifolds. Mathematics, 13(3), 444. https://doi.org/10.3390/math13030444

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Triple Mann Iteration Method for Variational Inclusions, Equilibria, and Common Fixed Points of Finitely Many Quasi-Nonexpansive Mappings on Hadamard Manifolds

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