On Some Inequalities Inspired by the Stability of Dynamical System

Zenon Moszner ()
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Zenon Moszner: Pedagogical University

Chapter Chapter 8 in Developments in Functional Equations and Related Topics, 2017, pp 161-170 from Springer

Abstract: Abstract We approximate the solutions of the system of inequalities | H ( t , H ( s , x ) ) − H ( t + s , x ) | ≤ δ , x ∈ I , t , s ∈ ℝ | H ′ ( 0 , x ) − a | ≤ δ , x ∈ I $$\displaystyle{ \left \{\begin{array}{ll} \vert H(t,H(s,x)) - H(t + s,x)\vert \leq \delta,\qquad &x \in I,t,s \in \mathbb{R}\\ \vert H'(0, x) - a\vert \leq \delta, \qquad &x \in I \end{array} \right. }$$ (I is nondegenerated interval) for a ≠ 0 by the dynamical system and we consider the different stabilities of this system for δ = 0.

Keywords: Generalized dynamical system; Stability; b-Stability; Inverse stability; Inverse b-stability; Absolute stability; Primary 39B82; Secondary 39B62 (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-319-61732-9_8

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DOI: 10.1007/978-3-319-61732-9_8

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