On Solving the Equilibrium Problem and Fixed Point Problem for Nonspreading Mappings and Lipschitzian Mappings in Hilbert Spaces

Sarawut Suwannaut

Abstract

The purpose of this research is to introduce and study the $S$-mapping generated by a finite family of nonspreading mappings and Lipschitzian mapping in a Hilbert space. Then, we prove a strong convergence theorem for finding a common element of the set of fixed points of a finite family of nonspreading mappings and Lipschitzian mappings and a common solution of a finite family of equilibrium problems. Futhermore, applying our main theorem, the additional results for equilibrium problem are obtained.