$\mu$-contractions in ordered metric spaces endowed with a $w_0$-distance

Abstract

We introduce in the setting of ordered metric spaces a new contractive condition called ordered $\mu$-contraction. We use such a condition in order to provide new and more generale results of existence and uniqueness of fixed point. We remark that from our main result one can easily deduce the Banach contraction principle, the Boyd-Wong result and other known results of fixed point in the existing literature.