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

In this paper, we apply self-adaptive methods to solve split pseudomonotone equilibrium problems subject to fixed point problems of 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.