Existence of solutions of infinite systems of nonlinear Volterra integral equations on a Fréchet space

Abstract

In this paper, we introduce a Fréchet space and define a measure of noncompactness on it. For credit and the application to our theorems, in the application section of this paper, we present a theorem which shows the existence of solution of infinite system of nonlinear Volterra integral equations, and by using the technique of measures of noncompactness together Darbo fixed point theorem we guarantee the existence of solution in this Fréchet space . Finally, we present some examples which show the efficiency and applicability of our theorem../files/site1/files/72/5Abstract.pdf

Keywords

• measure of noncompactness
• fréchet space
• darbo fixed point theorem
• infinite system of volterra integral equations.