The resolvent operator techniques with perturbations for finding zeros of maximal monotone operator and fixed point problems in Hilbert spaces

In this paper, we introduce iterative schemes with perturbations for finding zeros of the sum of two monotone operators and a fixed point problem of a nonexpansive mapping in Hilbert spaces. We prove a strong convergence theorem of the proposed iterative schemes under some certain conditions. Furthermore, we also apply our results to solving the variational inequality and equilibrium problems. The results obtained in this paper are improve and generalize many known recent results in this field.