HYBRID VISCOSITY APPROXIMATION METHODS WITH GENERALIZED CONTRACTIONS FOR ZEROS OF MONOTONE OPERATORS AND FIXED POINT PROBLEMS

In this paper, we construct implicit and explicit hybrid viscosity iterative algorithms with generalized contractions for approximating a common solution of the zero point problem with an inverse-strongly monotone mapping and a maximal monotone operator and the fixed point problem of an infinite family of nonexpansive mappings. Under suitable conditions, we obtain two strong convergence theorems in Hilbert space. Some applications and numerical examples are provided to support our main results.