# Strong Convergence of the Shrinking Projection Method for the Split Equilibrium Problem and an Infinite Family of Relatively Nonexpansive Mappings in Banach spaces

## Nutchari Niyamosot, Warunun Inthakon

## Keywords:

split equilibrium problem, equilibrium problems, relatively quasinonexpansive, relatively nonexpansive, common fixed point, shrinking projection method, Banach space## Abstract

In this paper, we use the shrinking projection method to prove a strong convergence theorem for finding a common solution of the split equilibrium problem and fixed point problem of a relatively quasi−nonexpansive mapping. Consequently, our main theorem can apply to find a common solution of the split equilibrium problem and common fixed point problem for an infinite family of relatively nonexpansive mappings in Banach spaces.

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## How to Cite

*Thai Journal of Mathematics*, 191–205. Retrieved from https://thaijmath2.in.cmu.ac.th/index.php/thaijmath/article/view/964