Engineering and Technology Journal

In this paper, we established weak convergence theorems by using appropriate conditions for approximating common fixed points and equivalence between the convergence of the Picard-Mann iteration scheme and Liu et al iteration scheme in Banach spaces. As well as, numerical examples are given to show that Picard-Mann is faster than Liu et al iteration schemes.

In this paper, sufficient conditions for controllability of nonlinear boundary value control system in Banach spaces are established. The results are obtained by using semigroup theory “compact semigroup”and some techniques of nonlinear functional analysis, such as, Schauderfixed point theorem. Moreover, example is provided to illustrate the theory.