An Investigation of an Integral Equation Involving Convex–Concave Nonlinearities

Ravi P. Agarwal, Mohamed Jleli and Bessem Samet
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Ravi P. Agarwal: Department of Mathematics, Texas A & M University-Kingsville, Kingsville, TX 78363, USA
Mohamed Jleli: Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
Bessem Samet: Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

Mathematics, 2021, vol. 9, issue 19, 1-10

Abstract: We investigate the existence and uniqueness of positive solutions to an integral equation involving convex or concave nonlinearities. A numerical algorithm based on Picard iterations is provided to obtain an approximation of the unique solution. The main tools used in this work are based on partial-ordering methods and fixed-point theory. Our results are supported by examples.

Keywords: integral equation; convex–concave nonlinearities; positive solution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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