Approximation of the Fixed Point of Multivalued Quasi-Nonexpansive Mappings via a Faster Iterative Process with Applications

Abstract

In this paper, we approximate the fixed points of multivalued quasi-nonexpansive mappings via a faster iterative process and propose a faster fixed-point iterative method for finding the solution of two-point boundary value problems. We prove analytically and with series of numerical experiments that the Picard–Ishikawa hybrid iterative process has the same rate of convergence as the CR iterative process.

A Robust Iterative Approach for Solving Nonlinear Volterra Delay Integro–differential Equations

“…We have also seen that the class of delay differential equation studied in [4,9,12,23,[25][26][27] is a special case of the class nonlinear Volterra delay integro-differential equation considered in this article. Hence, our results generalize, improve and unify the corresponding results in [4,9,12,15,[23][24][25][26][27][28] and several others in the existing literature.…”

“…Remark 1. Since the notion of w 2 -stability is more general the concept of simple stability considered in [15,24,28], hence, our result improves and generalizes the corresponding in [15,24,28] and several others.…”

“…In this paper, we have studied the stability result of our newly introduced iterative algorithm (1.9) for a wider concept of stability known as w 2 -stability instead of the simple notion of stability considered in [15,24,28]. A numerical example is also used to support the analytical proof of our stability theorem.…”

“…The authors proved numerically that (1.5) convergence is faster than each of Mann, Ishikawa, Noor, S, Abass iteration processes. Recently, Okeke et al [28] introduced the multivalued version of Picard-Ishikawa hybrid iterative algorithm which was considered in [26] as follows:…”

“…The notion of stability in Definition 6 has been studied by several authors for both single and multivalued mappings (see [15,24,28] and the references in them).…”