We generalize the notion of coupled fixed (or best proximity) points for cyclic ordered pairs maps to p-cyclic maps. find sufficient conditions existence and uniqueness points. illustrate results with an example that covers a wide class

Bhaskar and Lakshimkantham proved the existence of coupled fixed point for a single valued mapping under weak contractive conditions and as an application they proved the existence of a unique solution of a boundary value problem associated with a first order ordinary differential equation. Recently, Lakshmikantham and Ćirić obtained a coupled coincidence and coupled common fixed point of two s...

in this paper we prove a unique common coupled fixed point theorem for two pairs of $w$-compatible mappings in $s_b$-metric spaces satisfying a contrctive type condition. we furnish an example to support our main theorem. we also give a corollary for junck type maps.

Abstract This short note is on the question whether intersection of all fixed points a positive arithmetic operator and its closed can proved to be equivalent in weak fragment second order arithmetic.