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Abstract Objectives We explored the results of fixed point, coincidence point and coupled coincidence point for the mappings in an ordered metric spaces. Our results generalized and extended the well-known results in the literature. Some numerical examples are provided for justifying the results obtained. Result Some fixed point results are found for a self mapping in a partially ordered b-metric space which satisfies a generalized week contraction condition. Furthermore, these results are extended for two self mappings for obtaining coincidence point, coupled coincidence point and coupled common fixed point in the same context. A few examples are presented to support the findings.