Relatively Cyclic and Noncyclic <i>P</i>-Contractions in Locally K-Convex Space

Abstract

Our main goal of this research is to present the theory of points for relatively cyclic and relatively relatively noncyclic p-contractions in complete locally K -convex spaces by providing basic conditions to ensure the existence and uniqueness of fixed points and best proximity points of the relatively cyclic and relatively noncyclic p-contractions map in locally K -convex spaces. The result of this paper is the extension and generalization of the main results of Kirk and A. Abkar.

Keywords

• fixed point
• locally K-convex spaces
• relatively cyclic and relatively noncyclic p-contractions
• best proximity point