General viscosity implicit midpoint rule for nonexpansive mapping

In this work, we suggest a general viscosity implicit midpoint rule for nonexpansive mapping in the framework of Hilbert space. Further, under certain conditions imposed on sequence parameters, strong convergence theorem is proved by generated proposed iterative scheme, which, addition, unique solution variational inequality problem. Furthermore, provide some applications to inequalities, Fredholm integral equations, and nonlinear evolution equations give numerical example justify main result. The results presented work may be treated as an improvement, extension refinement corresponding ones literature.