A strong convergence theorem for solving an equilibrium problem and a fixed point problem using the Bregman distance

2021/09/08 by Ghadampour, Mostafa, Soori, Ebrahim, Agarwal, Ravi P. +1
#47H09 #47H10 #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2109.04245

Abstract

In this paper, using the Bregman distance, we introduce a new projection-type algorithm for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points. Then the strong convergence of the sequence generated by the algorithm will be established under suitable conditions. Finally, using MATLAB software, we present a numerical example to illustrate the convergence performance of our algorithm.

Related

• A new algorithm for mixed equilibrium problem and Bregman strongly nonexpansive mappings in Banach spaces
• A New Shrinking projection Algorithm for an infinite family of Bregman weak relatively nonexpansive mappings in a Banach Space
• Convergence theorem for solving generalized mixed equilibrium problem and finding fixed point of a weak Bregman relatively nonexpansive mapping in Banach spaces
• Strong convergence theorems by a new hybrid method for equilibrium problems and relatively nonexpansive mappings in Banach spaces
• A novel hybrid method for equilibrium problems and fixed point problems