On the Lebesgue integrable solution of an integral equation

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Published: 2026-02-18
DOI: https://doi.org/10.62754/ais.v7i1.1213
Keywords:
Schauder fixed point theorem, Kolmogorov theorem, Volterra integro-differential equation of convolution type, convex set, continuous operator.

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Mahmoud M. El-Borai
Department of Mathematics and Computer Science, Faculty of Science, Alexandria University, 21511 Alexandria, D Egypt
Wagdy G. El-Sayed
Department of Mathematics and Computer Science, Faculty of Science, Alexandria University, 21511 Alexandria, Egypt
Ahmed M. Ibrahim
Department of Mathematics and Computer Science, Faculty of Science, Alexandria University, 21511 Alexandria, Egypt
, Batoul E. AlFadhli
Department of Mathematics and Computer Science, Faculty of Science, Alexandria University, 21511 Alexandria, Egypt

Abstract

an existence theorem of a unique solution of a Volterra integral equation of convolution type will be
proved. The paper will be ended by two examples that treat the solvability of a Volterra integro-
differential equation of convolution type in the space of Lebesgue integrable functions L¹[ 0 ̦T ].

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Vol. 7 No. 1 (2026)

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Articles
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How to Cite

On the Lebesgue integrable solution of an integral equation. (2026). Architecture Image Studies, 7(1), 2302-2310. https://doi.org/10.62754/ais.v7i1.1213