Self-adaptive algorithms for solving split pseudomonotone equilibrium problems and pseudocontractive operators

Abstract

In this paper, we apply self-adaptive methods to solve split pseudomonotone equilibrium problems and pseudocontractive operators in Hilbert spaces.
 First, we use linear search rules to avoid the requirement of Lipschitz type conditions of bifunctions. Secondly, we just need to assume that two
 pseudocontractive operators are Lipschitz continuous, without knowing the sizes of the Lipschitz constants. We present a self-adaptive algorithm
 for solving the investigated split problem. Under some standard conditions, we show that the sequence generated by the algorithm converges weakly to a solution of the split problem.