Weak convergence theorem for finding fixed points and solution of split feasibility and systems of equilibrium problems
Summary: The purpose of this paper is to introduce an iterative algorithm for finding a common element of the set of fixed points of quasi-nonexpansive mappings and the solution of split feasibility problems (SFP) and systems of equilibrium problems (SEP) in Hilbert spaces. We prove that the sequences generated by the proposed algorithm converge weakly to a common element of the fixed points set of quasi-nonexpansive mappings and the solution of split feasibility problems and systems of equilibrium problems under mild conditions. Our main result improves and extends the recent ones announced by \textit{L.-C. Ceng} et al. [Comput. Math. Appl. 64, No. 4, 633--642 (2012; Zbl 1252.65102)] and many others.
scientific article; zbMATH DE number 6161335
scientific article