The main focus of this work is to assure that the sum of a compact operator with a Z-contraction admits a fixed point. The concept of condensing mapping (in the sense of Hausdorff non-compactness measure) is used to establish the concerned result which generalizes some of the existing state-of-art in the literature. Presented result is used to verify the actuality of solutions of implicit integral equations.


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Patel, Deepesh Kumar, Patle, Pradip R.