Hybrid proximal point algorithm for solving split equilibrium problems and its applications

Abstract

This paper deals with split equilibrium problems in Banach spaces. The presented algorithm is based on the hybrid algorithm and the proximal point algorithm and has been used for finding the solution of split equilibrium problems. Under some standard assumptions on equilibrium bifunctions, it is proven that the generated sequences by the presented scheme are strongly convergent. Finally, the efficiency of the proposed method is demonstrated through some examples. Also, comparative results verify that the proposed method is more effective than the other existing methods in the literature. Furthermore, an application of the presented algorithm in Hilbert spaces and an application of our method to solve the $LASSO$ problem in the field of compressed sensing are given.

Keywords

• split equilibrium problem
• strong convergence
• uniformly convex Banach space
• uniformly smooth Banach space

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