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Now these days, the utility of metric space and fixed point iterative techniques in computer sciences increased rapidly. Iterative results offer the mathematical root for a novel method to take out intricacy analysis of algorithms via metrics. This manuscript develops a new framework to derive common fixed point results, by replacing modified integral type contraction in metric spaces with an auxiliary function, without assuming continuity, commutative and compatible property of maps. Additionally, we demonstrate and tried to authenticate a theory which validates our result to deduce some innovative and interesting results that are novel in nature. To give some assistance to our findings, an illustrative example is given.