FIXED POINT ASSOCIATED WITH A NEW CLASS OF CONDENSING OPERATORS AND SOLVABILITY OF VOLTERRA INTEGRAL EQUATION HAVING DELAY - Nikam, V.E.; Mashale, J. D. (Journal of Nonlinear Analysis and Optimization: Theory & Applications (JNAO), 2025)
This work presents a novel class of condensing operators to explore the possibility of solutions for the Volterra integral equation with a singular kernel and proportional delay. These equations are significant in many domains, including engineering and physics, yet conventional solution techniques face substantial difficulties due to single kernels and delays. To solve this, we provide a more flexible method of handling such equations by creating a class of condensing operators based on pairs of functions that satisfy specific local requirements. We define these operators and also show some fixed point theorems that expand the application of Darbo’s fixed point theorem to a broader class of situations. At the end we provide examples to illustrate our theoretical results and show that the suggested approach works well.