Existence of Solution for Non-Linear Functional Integral Equations of Two Variables in Banach Algebra
Date
2019
Authors
Srivastava, H.M.
Das, Anupam
Hazarika, Bipan
Mohiuddine, S.A.
Journal Title
Journal ISSN
Volume Title
Publisher
Symmetry
Abstract
The aim of this article is to establish the existence of the solution of non-linear functional integral equations x(l,h)=(U(l,h,x(l,h))+F(l,h,∫l0∫h0P(l,h,r,u,x(r,u))drdu,x(l,h)))×G(l,h,∫a0∫a0Q(l,h,r,u,x(r,u))drdu,x(l,h)) of two variables, which is of the form of two operators in the setting of Banach algebra C([0,a]×[0,a]),a>0. Our methodology relies upon the measure of noncompactness related to the fixed point hypothesis. We have used the measure of noncompactness on C([0,a]×[0,a]) and a fixed point theorem, which is a generalization of Darbo’s fixed point theorem for the product of operators. We additionally illustrate our outcome with the help of an interesting example.
Description
Keywords
functional integral equations, Banach algebra, fixed point theorem, measure of noncompactness
Citation
Srivastava, H.M., Das, A., Hazarika, B. & Mohiuddine, S.A. (2019). Existence of Solution for Non-Linear Functional Integral Equations of Two Variables in Banach Algebra. Symmetry, 11(5), 674. https://doi.org/10.3390/sym11050674