Open AccessA coupled hybrid fixed point theorem involving the sum of two coupled operators in a partially ordered Banach space with applications
Author(s) -
Bapurao C. Dhage
Publication year - 2018
Publication title -
tamkang journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.324
H-Index - 18
eISSN - 0049-2930
pISSN - 2073-9826
DOI - 10.5556/j.tkjm.50.2019.2502
Subject(s) - mathematics , banach space , fixed point theorem , boundary value problem , fixed point , order (exchange) , mathematical analysis , nonlinear system , pure mathematics , picard–lindelöf theorem , physics , finance , quantum mechanics , economics
In this paper we prove a coupled hybrid fixed point theorem involving the sum of two coupled operators in a partially ordered Banach space and apply to a pair of nonlinear second order coupled linearly perturbed hybrid differential equations with the periodic boundary conditions for proving the existence and approximation of coupled solutions under certain mixed hybrid conditions. The abstract existence result of the coupled periodic boundary value problems is also illustrated by furnishing a numerical example.