Fixed point theorems for Kannan type mappings with applications to split feasibility and variational inequality problems

TL;DR

This paper introduces enriched Kannan mappings, extends fixed point theorems for these mappings, and applies them to develop algorithms for split feasibility and variational inequality problems in Banach spaces.

Contribution

It defines a new class of mappings called enriched Kannan mappings, extends fixed point results, and applies these to solve important problems in optimization.

Findings

Established convergence of Kransnoselskij iteration for enriched Kannan mappings.

Developed projection algorithms for split feasibility problems.

Extended results to enriched Bianchini mappings.

Abstract

The aim of this paper in to introduce a large class of mappings, called {\it enriched Kannan mappings}, that includes all Kannan mappings and some nonexpansive mappings. We study the set of fixed points and prove a convergence theorem for Kransnoselskij iteration used to approximate fixed points of enriched Kannan mappings in Banach spaces. We then extend further these mappings to the class of enriched Bianchini mappings. Examples to illustrate the effectiveness of our results are also given. As applications of our main fixed point theorems, we present two Kransnoselskij projection type algorithms for solving split feasibility problems and variational inequality problems in the class of enriched Kannan mappings and enriched Bianchini mappings, respectively.