We present sharp two-sided a-priori estimates for the solutions of a class of nonlinear Volterra integral equations in the cone of non-negative continuous functions. These estimates enable us to construct a complete metric space which is invariant under the nonlinear convolution operator considered here and to prove that the equation induced by this operator has a unique solution in this space as well as in the class of all non-negative continuous functions vanishing at the origin.
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Sultan N. Askhabov, M.A. Betilgiriev, A-Priori Estimates for the Solutions of a Class of Nonlinear Convolution Equations. Z. Anal. Anwend. 10 (1991), no. 2, pp. 201–204DOI 10.4171/ZAA/442