Estimation of Newly Established Iterative Scheme for Generalized Nonexpansive Mappings

Abstract

We introduce a new iterative method in this article, called the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"> <a:mi>D</a:mi> </a:math> iterative approach for fixed point approximation. Analytically, and also numerically, we demonstrate that our established <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" id="M2"> <c:mi>D</c:mi> </c:math> I.P is faster than the well-known I.P of the prior art. Finally, in a uniformly convex Banach space environment, we present weak as well as strong convergence theorems for Suzuki’s generalized nonexpansive maps. Our findings are an extension, refinement, and induction of several existing iterative literatures.