It is our purpose to continue the study of approximation of fixed point of multi- valued nonlinear mappings in a modular function space which is initiated by Khan and Abbas [14]. Some convergence results were established for three multi-valued ρ-quasi-nonexpansive mappings using a three step iterative scheme.

In this paper, the study of implicit viscosity approximation methods for non-expansive mappings in Banach spaces is explored. A new iterative sequence is introduced for the class of nonexpansive mappings in Banach spaces. Suitable conditions are imposed on the control parameters to prove a strong convergence theorem. Moreover, the strong convergence of the newly introduced sequence to a fixed point of a nonexpansive mapping is obtained which also solves the variational inequality problem. These results are improvement and extension of some recent corresponding results announced.