Some consequences of Caristi's fixed point theorem, partial answers to some known open problems and its applications

TL;DR

This paper explores extensions of Caristi's fixed point theorem, providing partial solutions to open problems and applications, including bounded solutions of functional equations, highlighting its significance in metric space analysis.

Contribution

It demonstrates how various extensions of Banach's contraction principle can be derived from Caristi's theorem and offers partial answers to open problems using its corollaries.

Findings

Extensions of Banach contraction principle derived from Caristi's theorem

Partial solutions to known open problems provided

Existence of bounded solutions to functional equations established

Abstract

In this paper, we show that several extension of Banach contraction principle, can be easily derived from the Caristi's theorem is one of the useful generalization of Banach contraction principle in the setting of the complete metric spaces. Moreover, some partial answers to some known open problems are given via Caristi's corollaries. Finally, existence of bounded solutions of a functional equation is studied to support our results.