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.

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The Thai Journal of Mathematics organized and supported by The Mathematical Association of Thailand and Thailand Research Council and the Center for Promotion of Mathematical Research of Thailand (CEPMART).

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|ISSN 1686-0209|