HYBRID FIXED POINT THEORY FOR SUM OF TWO OPERATORS IN A LATTICE ORDERED BANACH SPACE WITH APPLICATIONS TO NONLINEAR DISCONTINUOUS INTEGRAL EQUATIONS
By
Bapurao C. Dhage and Janhavi B. Dhage
Kasubai, Gurukul Colony, Thodga Road, Ahmedpur, Distr. Latur, Maharashtra, India- 413515
Email: bcdhage@gmail.com, jbdhage@gmail.com
(Received: August 08, 2025, Revised: May 03, 2026, Accepted: May 05, 2026)
DOI: https://doi.org/10.58250/jnanabha.2026.56112
Abstract
We prove a hybrid fixed point theorem for sum of two operators in a lattice ordered Banach space and apply to nonlinear discontinuous hybrid integral equations of mixed type for proving the existence of maximal and minimal integrable solutions under certain mixed Lipschitz and monotonicity conditions of the nonlinear functions. Our main existence result is illustrated with a numerical example as well as with an application to initial value problems of nonlinear first and second order discontinuous hybrid linearly perturbed ordinary differential equations for proving the existence of maximal and minimal solutions.
2020 Mathematical Sciences Classification: Primary 47H10; Secondary 45H05.
Keywords and Phrases: Lattice ordered Banach space; Hybrid fixed point principle; Nonlinear hybrid integral equation; Existence of extremal integrable solutions.