INERTIAL SELF ADAPTIVE ALGORITHM FOR SOLVING EQUILIBRIUM FIXED POINT AND PSEUDOMONOTONE VARIATIONAL INEQUALITY PROBLEMS IN HILBERT SPACES

ITERATIVE METHODS...

Abstract

In this paper, we study an iterative approximation of a common solution to equilibrium problem, fixed point problem and variational inequality problems. We introduced an inertial Tseng method with a viscosity approach for approximating a solution to the problem in a Hilbert space. The method is self adaptive so that it's execution does not rely on the Lipschitz condition of the cost operator. Under mild conditions, we show that the sequence generated by our algorithm converges strongly to a common solution of the fixed point and variational inequality problems associated with demicontractive and pseudomonotone operator which is also a solution to a generalized equilibrium problem. Our results extend and improve several existing results in the literature.