Asymptotic behavior of resolvents of equilibrium problems on complete geodesic spaces

• Autorzy: Kimura Yasunori , Shindo Keisuke

Identyfikatory

DOI

10.1515/dema-2022-0187

• Języki publikacji: EN

Abstrakty

EN

In this article, we discuss equilibrium problems and their resolvents on complete geodesic spaces. In particular, we consider asymptotic behavior and continuity of resolvents with positive parameter in a complete geodesic space whose curvature is bounded above. Furthermore, we apply these results to resolvents of convex functions.

Słowa kluczowe

EN

asymptotic behavior; geodesic space; convex function; resolvent

PL

zachowania asymptotyczne; przestrzeń geodezyjna; funkcja wypukła; rozpuszczalnik

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2023
• Tom: Vol. 56, nr 1
• Strony: art. no. 20220187
• Opis fizyczny: Bibliogr. 17 poz.

Twórcy

autor

Kimura Yasunori

• Department of Information Science, Toho University, Miyama, Funabashi, Chiba, 274-8510, Japan

autor

Shindo Keisuke

• Department of Information Science, Toho University, Miyama, Funabashi, Chiba, 274-8510, Japan

Bibliografia

• [1] W. Takahashi, Nonlinear Functional Analysis Fixed Point Theory and Its Applications, Yokohama Publishers, Yokohama, 2000.
• [2] S. Kamimura and W. Takahashi, Approximating solutions of maximal monotone operators in Hilbert spaces, J. Approx. Theory 106 (2000), 226–240.
• [3] S. Kamimura and W. Takahashi, Weak and strong convergence of solutions to accretive operator inclusions and applications, Set-Valued Anal. 8 (2000), 361–374.
• [4] S. Kamimura and W. Takahashi, Strong convergence of a proximal-type algorithm in a Banach space, SIAM J. Optim. 13 (2002), 938–945.
• [5] K. Kido, Strong convergence of resolvents of monotone operators in Banach spaces, Proc. Amer. Math. Soc. 103 (1988), 755–758.
• [6] R. G. Otero and B. F. Svaiter, A strongly convergent hybrid proximal method in Banach spaces, J. Math. Anal. Appl. 289 (2004), 700–711.
• [7] S. Reich, Constructive techniques for accretive and monotone operators, Applied Nonlinear Analysis (Proc. Third Internat. Conf. Univ. Texas, Arlington, Tex., 1978), Academic Press, New York, 1979, pp. 335–345.
• [8] S. Reich, Strong convergence theorems for resolvents of accretive operators in Banach spaces, J. Math. Anal. Appl. 75 (1980), 287–292.
• [9] Y. Kimura and Y. Kishi, Equilibrium problems and their resolvents in Hadamard spaces, J. Nonlinear Convex Anal. 19 (2018), no. 9, 1503–1513.
• [10] Y. Kimura, Resolvents of equilibrium problems on a complete geodesic space with curvature bounded above, Carpathian J. Math. 37 (2021), no. 3, 463–476.
• [11] S. Dhompongsa and B. Panyanak, On Delta-convergence theorems in CAT(0) spaces, Comput. Math. Appl. 56 (2008), no. 10, 2572–2579.
• [12] M. Asadi, S. Ghasemzadehdibagi, S. Haghayeghi, and N. Ahmad, Fixed point theorems for ( )a p, -nonexpansive mappings in CAT(0) spaces, Nonlinear Funct. Anal. Appl. 26 (2021), no. 5, 1045–1057.
• [13] M. Asadi, S. M. Vaezpour, and M. Soleymani, Some results for CAT(0) spaces, Theory Approx. Appl. 7 (2011), 11–19.
• [14] J. R. He, D. H. Fang, G. López, and C. Li, Mannas algorithm for nonexpansive mappings in CAT(kappa) spaces, Nonlinear Anal. 57 (2012), no. 2, 445–452.
• [15] S. Saejung, Halpern’s iteration in CAT(0) spaces, Fixed Point Theory and Appl. 2010 (2010), 13.
• [16] M. Bačák, Convex Analysis and Optimization in Hadamard Spaces, De Gruyter, Berlin, 2014.
• [17] Y. Kimura and K. Shindo, Asymptotic behavior of resolvents on complete geodesic spaces with general perturbation functions, Soft Computing and Optimization: SCOTA 2021, Ranchi, India (Springer Proceedings in Mathematics & Statistics), Springer Verlag, Singapore, 2022.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).