ON EXISTENCE OF EXTREMAL INTEGRABLE SOLUTIONS AND INTEGRAL INEQUALITIES FOR NONLINEAR URYSOHN TYPE INTEGRAL EQUATIONS
By
Janhavi B. Dhage, Shyam B. Dhage and Bapurao C. Dhage
Kasubai, Gurukul Colony, Thodga Road, Ahmedpur, Distr. Latur, Maharashtra, India-413515
Email: jbdhage@gmail.com, sbdhage4791@gmail.com, bcdhage@gmail.com
(Received: March 04, 2024; In format: March 11, 2024; Revised: November 16, 2024; Accepted: December 26, 2024)
DOI: https://doi.org/10.58250/jnanabha.2024.54230
Abstract
We prove the existence of maximal and minimal integrable solutions of nonlinear Urysohn type integral equations. Two basic integral inequalities are obtained in the form of extremal integrable solutions which are further exploited for proving the boundedness and uniqueness of the integrable solutions of the considered integral equation.
2020 Mathematical Sciences Classification: Primary 45G10 Secondary 47H10
Keywords: Urysohn integral equation; Tarski fixed point principle; Extremal integrable solutions; integral inequalities.