1. Some Fixed Point Theorems in Banach Spaces and Application to a Transport Equation with Delayed Neutrons
- Author
-
Khalid Latrach, Ahmed Zeghal, and Mohamed Yassine Abdallah
- Subjects
Pure mathematics ,General Mathematics ,010102 general mathematics ,Banach space ,Fixed-point theorem ,Type (model theory) ,Fixed point ,Mathematical proof ,01 natural sciences ,010101 applied mathematics ,Nonlinear system ,0101 mathematics ,Convection–diffusion equation ,Delayed neutron ,Mathematics - Abstract
In this paper, we present some fixed point theorems of Krasnosel’skii’s type in Banach spaces. The involved operators need not to be compact nor weakly continuous. The results are obtained and formulated with the use of the measures of weak noncompactness and a large classes of contractions (strict contractions, nonlinear contractions, as well as nonexpansive or pseudocontractive mappings). Throughout the paper, we use the hypothesis $$\mathsf {(H1)}$$ and $$\mathsf {(H2)}$$ , which are one of the main ingredients of the proofs. Finally, with the obtained fixed point results, we discuss the existence of solutions to a stationary transport equation with delayed neutrons.
- Published
- 2021