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 Analytical results for quadratic integral equations with phase--lag term M. A. Abdel-Aty,M. A. Abdou,A. A. Soliman Keywords:Quadratic integral equation, phase--lag, Tychonoff fixed point theorem, Banach space, fixed point theorem. Abstract: In the present paper, we are concerning with a quadratic integral equation with phase--lag term. In the following pages, sufficient conditions are given for the existence of positive continuous solution to quadratic integral equations. The method used here depends on both Tychonoff fixed point principle and Arzela--Ascoli theorem. A concrete example illustrating the mentioned applicability is also included.