Viscosity Approximation Methods for Split Variational Inclusion and Fixed Point Problems in Hilbert Spaces

The main objective of this paper is to find a common solution of split variational inclusion problem and fixed point problem of infinite family of nonexpansive operators in a setting of real Hilbert spaces. To reach this goal, the iterative algorithms which combine Moudafi’s viscosity approximation method with some fixed point technically proving methods are utilized for solving the problem. We prove that the iterative schemes with some suitable control conditions converge strongly to a common solution of the considered problem. We also show that many interesting problems can be solved by using our presented results.