Fixed Point Theory for Study the Controllability of Boundary Control Problems in Reflexive Banach Spaces

Riam  Bassem; Nassif  Al-Jawary

doi:10.24996/ijs.2022.63.1.23

Authors

Riam Bassem Department of Mathematics, Collage of Since, University of Al-Mustansiriya, Baghdad, Iraq
Nassif Al-Jawary Department of Mathematics, Collage of Since, University of Al-Mustansiriya, Baghdad, Iraq

DOI:

https://doi.org/10.24996/ijs.2022.63.1.23

Keywords:

Controllability, Reflexive Banach Space, Opial’s condition, Normal Structure, Semigroup Theory

Abstract

In this paper, we extend the work of our proplem in uniformly convex Banach spaces using Kirk fixed point theorem. Thus the existence and sufficient conditions for the controllability to general formulation of nonlinear boundary control problems in reflexive Banach spaces are introduced. The results are obtained by using fixed point theorem that deals with nonexpanisive mapping defined on a set has normal structure and strongly continuous semigroup theory. An application is given to illustrate the importance of the results.