On solving split mixed equilibrium problems and fixed point problems of hybrid-type multivalued mappings in Hilbert spaces

J Inequal Appl. 2017;2017(1):137. doi: 10.1186/s13660-017-1416-x. Epub 2017 Jun 15.

Abstract

In this paper, we introduce and study iterative algorithms for solving split mixed equilibrium problems and fixed point problems of λ-hybrid multivalued mappings in real Hilbert spaces and prove that the proposed iterative algorithm converges weakly to a common solution of the considered problems. We also provide an example to illustrate the convergence behavior of the proposed iteration process.

Keywords: Hilbert spaces; hybrid multivalued mappings; split mixed equilibrium problems; weak convergence.