International Journal of applied mathematics and computer science

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Paper details

Number 2 - June 2016
Volume 26 - 2016

Schauder’s fixed-point theorem in approximate controllability problems

Artur Babiarz, Jerzy Klamka, Michał Niezabitowski

The main objective of this article is to present the state of the art concerning approximate controllability of dynamic systems in infinite-dimensional spaces. The presented investigation focuses on obtaining sufficient conditions for approximate controllability of various types of dynamic systems using Schauder’s fixed-point theorem. We describe the results of approximate controllability for nonlinear impulsive neutral fuzzy stochastic differential equations with nonlocal conditions, impulsive neutral functional evolution integro-differential systems, stochastic impulsive systems with control-dependent coefficients, nonlinear impulsive differential systems, and evolution systems with nonlocal conditions and semilinear evolution equation.

approximate controllability, Banach space, Hilbert space, Schauder’s fixed-point theorem, infinite-dimensional space