Common Fixed Point of Generalizedweak Contractive Mappings in Partially Ordered $G_b$-Metric Spaces

Asadollah Aghajani, Mujahid Abbas, Jamal Rezaei Roshan

In this work, using the concepts of $G$-metric and $b$-metric we define a new type of metric which we call $G_b$-metric. We study some basic properties of such metric. We also prove a common fixed point theorem for six mappings satisfying weakly compatible condition in complete partially ordered $G_b$-metric spaces. A nontrivial example is presented to verify the e ectiveness and applicability of our main result.