Best proximity point for weak cyclic Kannan type $F-$contraction map and cyclic Chatterjea type $F-$contraction map

Abstract

In this paper, we introduce an innovative category of contractions termed "cyclic Chatterjea type $F-$contraction" and "weak cyclic Kannan type $F-$contraction." Subsequently, we establish a theorem for determining the best proximity point in a uniformly convex Banach space, specifically focusing on weak cyclic Kannan type $F-$contractions. Furthermore, we extend our investigation to include cyclic Chatterjea type $F-$contractions in uniformly convex Banach spaces. To support our findings, we present illustrative examples.

Keywords

• weak cyclic kannan type $f-$contraction, cyclic chatterjea type $f-$contraction, cyclic chatterjea type contraction, kannan type cyclic contraction, $f-$contraction, best proximity point.