Fixed point results of enriched interpolative Kannan type operators with applications

Abstract

The purpose of this paper is to introduce the class of enriched in- terpolative Kannan type operators on Banach space that contains the classes of enriched Kannan operators, interpolative Kannan type con- traction 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 approx- imate xed 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.