  Finding the solutions of nonlinear operator equations has been a subject of
research for decades but has recently attracted much attention. This paper
studies the convergence of a newly introduced viscosity implicit iterative
algorithm to a fixed point of a nonexpansive mapping in Banach spaces. Our
technique is indispensable in terms of explicitly clarifying the associated
concepts and analysis. The scheme is effective for obtaining the solutions of
various nonlinear operator equations as it involves the generalized
contraction. The results are applied to obtain a fixed point of
{\lambda}-strictly pseudocontractive mappings, solution of
{\alpha}-inverse-strongly monotone mappings, and solution of integral equations
of Fredholm type
