A SCHAUDER TYPE HYBRID FIXED POINT THEOREM IN A PARTIALLY ORDERED METRIC SPACE WITH APPLICATIONS TO NONLINEAR FUNCTIONAL INTEGRAL EQUATIONS
By
Bapurao C. Dhage
Kasubai, Gurukul Colony, Thodga Road, Ahmedpur-413515, District-Latur, Maharashtra, India
Email: bcdhage@gmail.com
(Received: June 01, 2022; In format : July 18, 2022; Revised : August 09, 2022; Accepted : November: 10, 2022)
DOI: https://doi.org/10.58250/jnanabha.2022.52220
Abstract
In this paper we prove some hybrid fixed point theorems for the monotonic nondecreasing mappings in a partially ordered metric space which includes the Schauder type fixed point theorems in an ordered Banach space proved by Dhage (2013,2014) and Dhage et al. (2022) in a partially ordered Banach space as the special cases. As an application, we discuss a nonlinear functional integral equation of Fredholm type and a nonlinear functional boundary value problem for proving the existence and approximation of solution by constructing the algorithms via Dhage monotone iteration method under some natural condtions.
2020 Mathematical Sciences Classification: 47H10, 34A08, 34A12, 34A34
Keywords and Phrases: Ordered metric space; Hybrid fixed point principle; Functional integral equation; Dhage iteration method; Existence and approximation theorem.