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Research Article | Open Access

An existence theorem for nonlinear functional Volterra integral equations via Petryshyn's fixed point theorem

Soniya Singh1, Satish Kumar2, Mohamed M. A. Metwali3, Saud Fahad Aldosary4, Kottakkaran S. Nisar4( )
Department of Applied Sciences and Engineering, Indian Institute of Technology Roorkee, Roorkee, India
Department of Applied Sciences, UIET, Panjab University SSG Regional Centre, Hoshiarpur (Punjab), India
Department of Mathematics, Faculty of Science, Damanhour Universty, Damanhour, Egypt
Department of Mathematics, College of Arts and Sciences, Wadi Aldawaser, 11991, Prince Sattam bin Abdulaziz University, Saudi Arabia
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Abstract

Using the method of Petryshyn's fixed point theorem in Banach algebra, we investigate the existence of solutions for functional integral equations, which involves as specific cases many functional integral equations that appear in different branches of non-linear analysis and their applications. Finally, we recall some particular cases and examples to validate the applicability of our study.

Keywords

Petryshyn's fixed point theoremmeasure of noncompactness (MNC)functional integral equation (FIE)
CLC number: 47H10

References

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AIMS Mathematics
Volume 7 Issue 4,
April 2022
Pages 5594-5604
DOI: 10.3934/math.2022309

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Cite this article:
Singh S, Kumar S, Metwali MMA, et al. An existence theorem for nonlinear functional Volterra integral equations via Petryshyn's fixed point theorem. AIMS Mathematics, 2022, 7(4): 5594-5604. https://doi.org/10.3934/math.2022309

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Received: 11 October 2021
Revised: 06 December 2021
Accepted: 13 December 2021
Published: 15 April 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)