Paired-Kannan contraction mappings and fixed point results

Abstract

We introduce a novel contraction concept for mappings within metric spaces called Paired-Kannan contraction. Unlike traditional Kannan contraction mappings, which involve two points, Paired-Kannan contraction mappings extend this concept to three points. We explore their properties, noting that while these mappings may generally be discontinuous, they exhibit continuity at fixed points akin to Kannan contractions. Importantly, we establish that Paired-Kannan contraction mappings constitute distinct entities from traditional Kannan contractions. We prove a fixed point theorem for Paired Kannan contraction mappings and show that conditions like asymptotic regularity and continuity extend these theorems' applicability. Additionally, we derive two new fixed point theorems for these mappings, applicable even in non-complete metric spaces.