Results 1 to 10 of about 3,894 (258)
On Hyperstability of the Cauchy Functional Equation in n-Banach Spaces [PDF]
Mathematics, 2020 We present some hyperstability results for the well-known additive Cauchy functional equation f(x+y)=f(x)+f(y) in n-normed spaces, which correspond to several analogous outcomes proved for some other spaces. The main tool is a recent fixed-point theorem.
Janusz Brzdęk, El-sayed El-hady
doaj +3 more sources
Some hyperstability and stability results for the Cauchy and Jensen equations
Journal of Inequalities and Applications, 2022 In this paper we give some hyperstability and stability results for the Cauchy and Jensen functional equations on restricted domains. We provide a simple and short proof for Brzdȩk’s result concerning a hyperstability result for the Cauchy equation.
Mohammad Bagher Moghimi, Abbas Najati
doaj +3 more sources
Hyperstability and Superstability [PDF]
Abstract and Applied Analysis, 2013 Summary: This is a survey paper concerning the notions of hyperstability and superstability, which are connected to the issue of Ulam's type stability. We present the recent results on those subjects.
Janusz Brzdęk, Krzysztof Ciepliński
doaj +4 more sources
Computation, 2023 This paper investigates the asymptotic hyperstability of a single-input–single-output closed-loop system whose controlled plant is time-invariant and possesses a strongly strictly positive real transfer function that is subject to internal and external ...
Manuel De la Sen
doaj +2 more sources
Hyers–Ulam stability and hyperstability of a Jensen-type functional equation on 2-Banach spaces
Journal of Inequalities and Applications, 2022 The main aim of this paper is to establish the Hyers–Ulam stability and hyperstability of a Jensen-type quadratic mapping in 2-Banach spaces. That is, we prove the various types of Hyers–Ulam stability and hyperstability of the Jensen-type quadratic ...
Arumugam Ponmana Selvan, Abbas Najati
doaj +2 more sources
Hyperstability of Some Functional Equations on Restricted Domain [PDF]
Journal of Function Spaces, 2017 The paper concerns functions which approximately satisfy, not necessarily on the whole linear space, a generalization of linear functional equation. A Hyers-Ulam stability result is proved and next applied to give conditions implying the hyperstability ...
Anna Bahyrycz, Jolanta Olko
doaj +2 more sources
Hyperstability of Cauchy and Jensen functional equations in 2-normed spaces
Journal of Inequalities and ApplicationsIn this article, with simple and short proofs without applying fixed point theorems, some hyperstability results corresponding to the functional equations of Cauchy and Jensen are presented in 2-normed spaces.
Abbas Najati +3 more
doaj +2 more sources
On an equation characterizing multi-cubic mappings and its stability and hyperstability [PDF]
Fixed Point Theory, 2021 In this paper, we introduce $n$-variables mappings which are cubic in each variable. We show that such mappings satisfy a functional equation. The main purpose is to extend the applications of a fixed point method to establish the Hyers-Ulam stability ...
Abasalt Bodaghi, Behrouz Shojaee
openalex +3 more sources
Mathematics, 2022 This paper visualizes the role of hyperstable controllers in the closed-loop asymptotic stability of a single-input single-output system subject to any nonlinear and eventually time-varying controller within the hyperstable class.
Manuel De la Sen
doaj +2 more sources
Enhanced Vigilance Stability during Daytime in Insomnia Disorder [PDF]
Brain Sciences, 2020 Central nervous hyperarousal is as a key component of current pathophysiological concepts of chronic insomnia disorder. However, there are still open questions regarding its exact nature and the mechanisms linking hyperarousal to sleep disturbance. Here,
Ariane Losert +6 more
doaj +2 more sources