Fixed points for three point generalized orbital triangular contractions

TL;DR

This paper introduces new classes of mappings called generalized orbital triangular contractions in metric spaces, proving their fixed point properties and extending to related contraction types, broadening fixed point theory.

Contribution

It defines and analyzes generalized orbital triangular contractions, extending fixed point results to non-continuous mappings and related contraction classes.

Findings

Unique fixed points under certain conditions

Mappings are not necessarily continuous

Extension to Kannan and Chatterjea contractions

Abstract

In this paper we introduce and study new classes of mappings in metric spaces. The main class of mappings is called generalized orbital triangular contractions and it generalizes some existing results (such as Banach contractions, mappings contracting perimeters of triangles). We prove that these contractions are not necessarily continuous and have a unique fixed point under certain conditions. Moreover, we extend our class to generalized orbital triangular Kannan contractions and generalized orbital triangular Chatterjea contractions.