Compatible mappings and its variants satisfying generalized (ψ, φ)−weak contraction

Abstract

Banach contraction principle behaves as a mathematical tool to solve various practical problems arising during mathematical formulation of many theoretical problems. In present work, the existence of a unique common fixed point for pairs of minimal commutative mappings is discussed, which satisfy a generalized (ψ, φ)−weak contraction involving cubic terms of distance functions. Examples are given in support of the obtained results and as an application the existence of solution of system of certain functional equations arising in dynamic programming is discussed.

Keywords

• generalized (ψ, φ)-weak contraction
• compatible mappings
• minimal commutative mappings, functional equations