Solutions of Equilibrium Problems with Fixed Point Iteration Method and Data Dependence

Source abstract

In this paper, we give comprehensive details about iteration methods to solve equilibrium problems through viscosity type approximation. This study introduces a new viscosity type iteration method in order to find the common point of the set of fixed points of nonexpansive mappings and relaxed $(a,b)$-cocoercive mapping, and the groups of solutions for of variational inequality and an equilibrium problem in Hilbert spaces. We also argue that this iteration method strongly converges to a common point in the mentioned three sets. As part of the applications, we give an example supporting the convergence theorem. As we emphasize the concept of data dependency for fixed point theory, we present the data dependence result for the fixed points of the stated class of mappings for the novel iteration method via viscosity type approximation.