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

Soniya Singh; Satish Kumar; Mohamed M. A. Metwali; Saud Fahad Aldosary; Kottakkaran S. Nisar; Soniya Singh; Satish Kumar; Mohamed M. A. Metwali; Saud Fahad Aldosary; Kottakkaran S. Nisar

doi:10.3934/math.2022309

AIMS Mathematics

2022, Volume 7, Issue 4: 5594-5604. doi: 10.3934/math.2022309

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Research article

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

1.
Department of Applied Sciences and Engineering, Indian Institute of Technology Roorkee, Roorkee, India
2.
Department of Applied Sciences, UIET, Panjab University SSG Regional Centre, Hoshiarpur (Punjab), India
3.
Department of Mathematics, Faculty of Science, Damanhour Universty, Damanhour, Egypt
4.
Department of Mathematics, College of Arts and Sciences, Wadi Aldawaser, 11991, Prince Sattam bin Abdulaziz University, Saudi Arabia

Received: 11 October 2021 Revised: 06 December 2021 Accepted: 13 December 2021 Published: 10 January 2022
MSC : 47H10

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.
- Petryshyn's fixed point theorem,
- measure of noncompactness (MNC),
- functional integral equation (FIE)
Citation: Soniya Singh, Satish Kumar, Mohamed M. A. Metwali, Saud Fahad Aldosary, Kottakkaran S. Nisar. An existence theorem for nonlinear functional Volterra integral equations via Petryshyn's fixed point theorem[J]. AIMS Mathematics, 2022, 7(4): 5594-5604. doi: 10.3934/math.2022309

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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.

References

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