On solvability for two-dimensional non-linear functional integral equations via measure of non-compactness

Volume 18, Issue 1, pp 20--28 https://dx.doi.org/10.22436/jnsa.018.01.02

Publication Date: November 15, 2024 Submission Date: July 05, 2024 Revision Date: August 19, 2024 Accteptance Date: September 23, 2024

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Authors

R. Kumar - Department of Mathematics, Applied Science and Humanities, Delhi Skill and Entrepreneurship University, New Delhi-110077, India. B. Singh - Department of Mathematics, PM College of Excellence, MJS Government PG College, Bhind Madhya Pradesh- 477001, India. S. Kumar - Department of Mathematics, PDPM Indian Institute of Information Technology, Design \(\&\) Manufacturing Jabalpur, Madhya Pradesh- 482005, India. - Department of Mathematics, Graphic Era Hill University, Dehradun Uttarakhand-248002, India.

Abstract

In this paper, we find out conditions for the existence result of two dimensional generalized functional integral equations in \(C([0, c]\times [0, d])\). The main theorem is proved by using the theory of Petryshyn's fixed point theorem and measure of non-compactness. A few examples of equations is provided to show the applicability in various integral equations.

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Keywords

• Functional integral equation
• fixed point theorem
• Banach algebra
• measure of non-compactness

MSC

•  45A05

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