Existence of Common Fixed point for $b$-Metric Rational Type Contraction

Abstract

The necessary conditions for existence of
a common fixed point of two mappings satisfying generalized $b$-order contractive
condition in the setting of a partially ordered $b$-complete $b$-metric space are presented. Also, we study well-posedness of common fixed
point problem for generalized $b$-order contractive mappings. We employ our
result to establish an existence of a solution of an integral equation.