Approximating the fixed points of Suzuki's generalized non-expansive map via an efficient iterative scheme with an application

This paper is aimed at proving the efficiency of a faster iterative scheme called PC^*-iterative scheme to approximate the fixed points for the class of Suzuki's Generalized non-expansive mapping in a uniformly convex Banach space. We will prove some weak and strong convergence results. It is justified numerically that the PC^*-iterative scheme converges faster than many other remarkable iterative schemes. We will also provide numerical illustrations with graphical representations to prove the efficiency of PC^* iterative scheme. As an application of the solution of a fractional differential equation is obtained by using PC^* iterative scheme.