Fixed point results of enriched interpolative Kannan type operators with applications

TL;DR

This paper introduces a new class of nonlinear operators called enriched interpolative Kannan type operators on Banach spaces, proves convergence of an iterative method for fixed points, and applies these results to variational inequality problems.

Contribution

It defines a novel class of operators that unify several existing classes and establishes their fixed point properties and stability, with applications to variational inequalities.

Findings

Convergence of Krasnoselskii iteration for these operators

Well-posedness and stability results established

Application to solving variational inequality problems

Abstract

The purpose of this paper is to introduce the class of enriched interpolative Kannan type operators on Banach space that contains the classes of enriched Kannan operators, interpolative Kannan type contraction operators and some other classes of nonlinear operators. Some examples are presented to support the concepts introduced herein. A convergence theorem for the Krasnoselskii iteration method to approximate fixed point of the enriched interpolative Kannan type operators is proved. We study well-posedness, Ulam-Hyers stability and periodic point property of operators introduced herein. As an application of the main result, variational inequality problem is solved.