Viscosity approximation with generalized contractions for fixed point problems and split fixed point problems of nonlinear operators

Abstract

In this paper, we construct the hybrid viscosity iterative algorithms with generalized contraction to approximate the fixed point of nonlinear operators such as demicontractive operators. Under appropriate conditions, we establish the corresponding strong convergence theorems. Moreover, we apply our results to approximating the common fixed points of nonlinear operators and solving the split common fixed point problems of nonlinear operators. Finally, we present numerical examples to demonstrate the convergence of our algorithm.