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In this paper, the concept of contraction via the measure of non-compactness on a Banach space is investigated by generalizing some results which have been previously discussed in literatures. Furthermore, to validity of the theorems and homotopy perturbation method (HPM), as a technical solution, they are applied on some nonlinear singular integral equations.
In this paper, we prove some fixed point theorems for infinite families of self-mappings of a complete metric space satisfying some new conditions of common contractivity. An example is presented to show the effectiveness of our results.
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