Stability Results and Reckoning Fixed Point Approaches by a Faster Iterative Method with an Application

Abstract

In this manuscript, we investigate some convergence and stability results for reckoning fixed points using a faster iterative scheme in a Banach space. Also, weak and strong convergence are discussed for close contraction mappings in a Banach space and for Suzuki generalized nonexpansive mapping in a uniformly convex Banach space. Our method opens the door to many expansions in the problems of monotone variational inequalities, image restoration, convex optimization, and split convex feasibility. Moreover, some experimental examples were conducted to gauge the usefulness and efficiency of the technique compared with the iterative methods in the literature. Finally, the proposed approach is applied to solve the nonlinear Volterra integral equation with a delay.