On the solvability of a nonlinear functional integral equations via measure of noncompactness in

Wagdy G.  El-Sayed; Mahmoud M.  El-Borai; Mohamed M.A.  Metwali; Nagwa I.  Shemais

doi:10.24297/jam.v19i.8885

Authors

Wagdy G. El-Sayed Faculty of Science, Alexandria University, Alexandria, Egypt https://orcid.org/0000-0003-3527-0206
Mahmoud M. El-Borai Faculty of Science, Alexandria University, Alexandria, Egypt
Mohamed M.A. Metwali Department of mathematics, Faculty of Science, Damanhour Universty, Egypt
Nagwa I. Shemais Department of mathematics, Faculty of Science, Damanhour Universty, Egypt

DOI:

https://doi.org/10.24297/jam.v19i.8885

Keywords:

functional integral equation, Darbo’s fixed point theorem, measure of noncompactnes; existence, fixed point

Abstract

Using the technique of a suitable measure of non-compactness and the Darbo fixed point theorem, we investigate the existence of a nonlinear functional integral equation of Urysohn type in the space of Lebesgue integrable functions L^p(R^N). In this space, we show that our functional-integral equation has at least one solution. Finally, an example is also discussed to indicate the natural realizations of our abstract result.

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