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In this paper, a generalization of Diaz-Margolis’s fixed point theorem is established. As applications of the generalized Diaz-Margolis’s fixed point theorem, we present some existence theorems of the Hyers-Ulam stability for a general class of the nonlinear Volterra integral equations in Banach spaces.

A generalization of Diaz-Margolis’s fixed point theorem and its application to the stability of generalized Volterra integral equations