Common solution for a finite family of equilibrium problems, finite family of inclusion problems and fixed points of a nonexpansive mapping in hadamard manifolds

  • Prashant Patel Department of Mathematics, School of Advanced Sciences, VIT-AP University.
  • Rahul Shukla Department of Mathematical Sciences & Computing, Walter Sisulu University, South Africa https://orcid.org/0000-0002-9835-0935

Résumé

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.

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Références

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).

Publiée
2025-02-22
Rubrique
Research Articles