On solving split equilibrium problems and fixed point problems of α-nonexpansive multi-valued mappings in Hilbert spaces



	On solving split equilibrium problems and fixed point problems of α-nonexpansive multi-valued mappings in Hilbert spaces


	Fixed Point Theory, Volume 24, No. 2, 2023, 641-660, June 15th, 2023 DOI: 10.24193/fpt-ro.2023.2.12 Authors: Yang Li, Congjun Zhang and Yuehu Wang Abstract: In this paper, we introduce α-nonexpansive multi-valued mappings in Hilbert spaces, and prove some properties and the existence of fixed points of these mappings. Further, we apply the Fan-KKM theorem to prove the existence of solutions to split equilibrium problems. Then we study iterative schemes for solving split equilibrium problems and common fixed point problems of a finite family of α-nonexpansive multi-valued mappings in Hilbert spaces. we prove that the proposed iterative algorithms converge weakly and strongly to a common solution of the considered problems. Our results improve and extend the previous results given in the literature. Key Words and Phrases: α-nonexpaxnsive multi-valued mapping, split equilibrium problem, fixed point. 2010 Mathematics Subject Classification: 47H10, 54H25, 47J25. Published on-line: June 15th, 2023. Fulltext pdf Back to volume's table of contents