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2 Journal of Mathematics and Applications

2 2020

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Solvability of a quadratic integral equation of Fredholm type via a modified argument

Dal İlyas, Temizer Ӧmer Faruk

Journal of Mathematics and Applications

2020

Vol. 43

47--66

This article concerns with the existence of solutions of thea quadratic integral equation of Fredholm type with a modified argument, [wzór], where p, k are functions and F is an operator satisfying the given conditions. Using the properties of the Hölder spaces and the classical Schauder fixed point theorem, we obtain the existence of solutions of the equation under certain assumptions. Also, we present two concrete examples in which our result can be applied.

On the existence of continuous positive monotonic solutions of a self-reference quadratic integral equation

El-Sayed Ahmed M.A., Ebead Hanaa R.

Journal of Mathematics and Applications

2020

Vol. 43

67--80

In this work we study the existence of positive monotonic solutions of a self-reference quadratic integral equation in the class of continuous real valued functions. The continuous dependence of the uniquesolution will be proved. Some examples will be given.