On New Generalized Viscosity Implicit Double Midpoint Rule for Hierarchical Problem

The implicit midpoint rules are employed as a powerful numerical technique, and in this article we attend class of viscosity iteration approximations on hierarchical problems for the double rules. We prove strong convergence theorem to unique solution problem technique is established under some favorable conditions imposed control parameters Hilbert spaces. Furthermore, propose applications constrained convex minimization problem, nonlinear Fredholm integral equation variational inequality fixed point problem. Moreover, examples also presented illustrate different proposed methods results. Our results modified with