On solving split equilibrium problems and fixed point problems of α-nonexpansive multi-valued mappings in Hilbert spaces
Li Yang, Zhang Congjun, Wang Yuehu · Fixed Point Theory · 2023
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.