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Common Fixed Point of Generalized Weak Contractive Mappings in Partially Ordered G b-metric Spaces

In this work, using the concepts of G-metric and b-metric we define a new type of metric which we call Gb-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 Gb-metric spaces. A nontrivial example is presented to verify the effectiveness and applicability of our main result.