Existence of solutions of implicit integral equations via Z-contraction

Source abstract

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.