A generalization of Kannan and Fisher fixed point theorems with an application to Volterra type integral equations

TL;DR

This paper extends classical fixed point theorems by Kannan and Fisher to more general settings, establishing new connections and applying these results to solve Volterra type integral equations.

Contribution

It introduces a broad generalization of Kannan and Fisher fixed point theorems and explores their relationship in specialized metric spaces, with applications to integral equations.

Findings

Generalized fixed point theorems for Kannan and Fisher types

Established connection between continuous Kannan and Fisher operators

Applied theorems to solve Volterra type integral equations

Abstract

In this paper, we discuss about the independent types of infinite extensions to a general version of Kannan [5] and Fisher [3] of which the well-known Kannan and Fisher theorems come as a corollaries. We also provide a strong connection between continuous Kannan operator and Fisher operator in a restricted type of metric space. We also provide an application of the main theorem of this paper, in the field of integral equations.