Common solution for a finite family of equilibrium problems, finite family of inclusion problems and fixed points of a nonexpansive mapping in hadamard manifolds
Abstract
The purpose of this paper is to showcase an iterative algorithm and demonstrate that the sequence produced by it converges robustly to a common solution of a finite collection of equilibrium problems, a finite collection of quasi-variational inclusion problems, and a set of fixed points of a nonexpansive mapping.
Downloads
References
S. Al-Homidan, Q. H. Ansari, and F. Babu, Halpern and Mann type algorithms for fixed points and inclusion problems on Hadamard manifolds, Numer. Funct. Anal. Optim., 40(6):621–653, (2019).
Q. H. Ansari, F. Babu, and X. Li, Variational inclusion problems in Hadamard manifolds, J. Nonlinear Convex Anal., 19(2):219–237, (2018).
E. Blum and W. Oettli, From optimization and variational inequalities to equilibrium problems, Math. Student, 63(1-4):123–145, (1994).
S. Chang, J. C. Yao, L. Yang, C. F. Wen, and D. P. Wu, Convergence analysis for variational inclusion problems equilibrium problems and fixed point in Hadamard manifolds, Numer. Funct. Anal. Optim., 42(5):567–582, (2021).
S. S. Chang, Existence and approximation of solutions for set-valued variational inclusions in Banach space, In Proceedings of the Third World Congress of Nonlinear Analysts, Part 1 (Catania, 2000), volume 47, pages 583–594, (2001).
S. S. Chang, J. Tang, and C. Wen, A new algorithm for monotone inclusion problems and fixed points on Hadamard manifolds with applications, Acta Math. Sci. Ser. B (Engl. Ed.), 41(4):1250–1262, (2021).
V. Colao, G. Lopez, G. Marino, and V. Martın-Marquez, Equilibrium problems in Hadamard manifolds, J. Math. Anal. Appl., 388(1):61–77, (2012).
V. Colao, G. Lopez, G. Marino, and V. Martın-Marquez, Equilibrium problems in Hadamard manifolds J. Math. Anal. Appl., 388(1):61–77, (2012).
J. X. da Cruz Neto, O. P. Ferreira, and L. R. Lucambio Perez, Monotone point-to-set vector fields, Balkan J. Geom. Appl., 5(1):69–79, (2000).
O. P. Ferreira and P. R. Oliveira, Proximal point algorithm on Riemannian manifolds, Optimization, 51(2):257–270, (2002).
S. Kamimura and W. Takahashi, Approximating solutions of maximal monotone operators in Hilbert spaces, J. Approx. Theory, 106(2):226–240, (2000).
K. Khammahawong, P. Kumam, and P. Chaipunya, Splitting algorithms of common solutions between equilibrium and inclusion problems on hadamard manifolds, arXiv preprint arXiv:1907.00364, (2019).
C. Li, G. Lopez, and V. Martın-Marquez, Monotone vector fields and the proximal point algorithm on Hadamard manifolds, J. Lond. Math. Soc. (2), 79(3):663–683, (2009).
C. Li, G. Lopez, V. Martın-Marquez, and J. H. Wang, Resolvents of set-valued monotone vector fields in Hadamard manifolds, Set-Valued Var. Anal., 19(3):361–383, (2011).
S. Z. Nemeth, Monotone vector fields, Publ. Math. Debrecen, 54(3-4):437–449, (1999).
W. Oettli, A remark on vector-valued equilibria and generalized monotonicity, Acta Math. Vietnam., 22(1):213–221, (1997).
R. Pant, R. Shukla, and P. Patel, Nonexpansive mappings, their extensions, and generalizations in Banach spaces, In Metric Fixed Point Theory, pages 309–343. Springer, (2021).
P. Patel and R. Shukla, Mann-Dotson’s algorithm for a countable family of non-self Lipschitz mappings in hyperbolic metric space, Topol. Algebra Appl., 11(1):20220134, 13, (2023).
P. Patel and R. Shukla, Common solution for a finite family of equilibrium problems, inclusion problems and fixed points of a finite family of nonexpansive mappings in hadamard manifolds, Sahand Communications in Mathematical Analysis, 21(1):255–271, (2024).
P. Patel and R. Shukla, Mann–Dotson’s algorithm for a countable family of non-self strict pseudo-contractive mappings, Rend. Circ. Mat. Palermo (2), 73(1):225–240, (2024).
R. T. Rockafellar, Monotone operators and the proximal point algorithm, SIAM J. Control Optim., 14(5):877–898, (1976).
D. R. Sahu, Q. H. Ansari, and J. C. Yao, The prox-Tikhonov-like forward-backward method and applications, Taiwanese J. Math., 19(2):481–503, (2015).
T. Sakai, Riemannian geometry, Translations of Mathematical Monographs, 149 (1996).
J. Zhu, J. Tang, S. S. Chang, M. Liu, and L. Zhao, Common solution for a finite family of equilibrium problems, quasi-variational inclusion problems and fixed points on hadamard manifolds, Symmetry, 13(7):1161, (2021).
Copyright (c) 2025 Boletim da Sociedade Paranaense de Matemática

This work is licensed under a Creative Commons Attribution 4.0 International License.
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).



