A Fixed Point Theorems in Banach Algebra with Applications to Functional Integral Equations

Mohamed Amine Farid; Marhrani El Miloudi; Chaira Karim and Aamri Aamri; Academic Editor: Youssef EL FOUTAYENI

Research Communication | Open Access
Volume 2019 | Communication ID 104

A Fixed Point Theorems in Banach Algebra with Applications to Functional Integral Equations

Mohamed Amine Farid, Marhrani El Miloudi, Chaira Karim and Aamri Aamri

Academic Editor: Youssef EL FOUTAYENI

Received	Accepted	Published
Jan 25, 2019	Feb 26, 2019	Mar 01, 2019

Abstract: Fixed point theory is an important topic and the core part of nonlinear functional analysis and the theories of differential and integral equations. Some of these equations can be formulated into one of nonlinear operator equations x=Ax+Bx, x=AxBx+Cx, x=AxBx+AxDx+Cx. The resolution of these equations was the main interest of many scientists and there results were very interesting. In this work we get unified results for solving these equations, for this, we introduce new family operators in these equations. As an application, we give an example of a functional nonlinear integral ...