ON INTEGRO-DIFFERENTIAL EQUATIONS VIA MEIR-KEELER CONDENSING OPERATORS AND THE MEASURE OF NONCOMPACTNESS*

Kattar Enada Bensatal[1], Abdelkrim Salim[2],

Mouffak Benchohra[3]

Abstract. This paper discusses the existence of solution for integro-differential equations via resolvent operators in Banach space. Our approach is based on a new fixed point theorem with respect to Meir-Keeler condensing operators. An example is given to show the application of our result.

MSC: 45J05, 47G20, 34G20, 37C25, 54H25, 58C30, 47H10, 55M20, 47H08

Keywords: Integro-differential equation; resolvent operator; Meir-Keeler condensing operators.

DOI 10.56082/annalsarscimath.2024.1.43

Abstract Article Volume 16 no 1 / 2024

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*Accepted for publication on January 10-th, 2023

[1] nadabensatal@gmail.com Laboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbes, P.O. Box 89, Sidi Bel-Abbes 22000, Algeria

[2] salim.abdelkrim@yahoo.com Faculty of Technology, Hassiba Benbouali University of Chlef, P.O. Box 151 Chlef 02000, Algeria

[3] benchohra@yahoo.com Laboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbes, P.O. Box 89, Sidi Bel-Abbes 22000, Algeria