Results 91 to 100 of about 1,022 (204)

On Ulam's Type Stability of the Cauchy Additive Equation

The Scientific World Journal, 2014
We prove a general result on Ulam's type stability of the functional equation fx+y=fx+fy, in the class of functions mapping a commutative group into a commutative group. As a consequence, we deduce from it some hyperstability outcomes.
Janusz Brzdęk
doaj   +1 more source

On asymptotic behaviors of a specific cubic functional equation and its hyperstability

Demonstratio Mathematica
In this article, the asymptotic behavior and hyperstability of the cubic functional equation f(2x+y)+f(2x−y)=2f(x+y)+2f(x−y)+12f(x) $$f\left(2x+y\right)+f\left(2x-y\right)=2f\left(x+y\right)+2f\left(x-y\right)+12f\left(x\right)$$ are discussed.
Bae Jae-Hyeong, Najati Abbas, Tareeghee Mohammad Amin   +2 more
doaj   +1 more source

HyperSteer: Activation Steering at Scale with Hypernetworks

CoRR
Steering language models (LMs) by modifying internal activations is a popular approach for controlling text generation. Unsupervised dictionary learning methods, e.g., sparse autoencoders, can be scaled to produce many steering vectors, but lack guarantees on the individual efficacy of each vector and control over the coverage of relevant steering ...
Jiuding Sun, Sidharth Baskaran, Zhengxuan Wu, Michael Sklar, Christopher Potts, Atticus Geiger   +5 more
openaire   +3 more sources

Approximate solution of generalized inhomogeneous radical quadratic functional equations in 2-Banach spaces

Journal of Inequalities and Applications, 2019
In this paper, using Brzdȩk and Ciepliński’s fixed point theorems in a 2-Banach space, we investigate approximate solution for the generalized inhomogeneous radical quadratic functional equation of the form f(ax2+by2)=af(x)+bf(y)+D(x,y), $$f \bigl(\sqrt{
Yali Ding, Tian-Zhou Xu
doaj   +1 more source

Stability of the Apollonius Type Additive Functional Equation in Modular Spaces and Fuzzy Banach Spaces

Mathematics, 2019
In this work, we investigate the generalized Hyers-Ulam stability of the Apollonius type additive functional equation in modular spaces with or without Δ 2 -conditions.
Sang Og Kim, John Michael Rassias
doaj   +1 more source

Absolute stability and hyperstability of a class of hereditary systems

Informatica, 1998
This paper extends some basic results on absolute stability and hyperstability from linear plants subject to a wide class of nonlinear controllers to plants having delays in the state while being controlled by the same classes of nonlinear controllers.
Manuel de la Sen, Josu Jugo
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Hyperstability of some functional equations in modular spaces [PDF]

In this paper, we investigate some hyperstability results, inspired by the concept of Ulam stability, for the following functional equations: \begin{equation} φ(x+y)+φ(x-y)=2φ(x)+2φ(y) \end{equation} \begin{equation} φ(ax+by) = Aφ(x)+Bφ(y)+C \end ...
Rossafi, Mohamed, Baza, Abderrahman, Mouniane, Mohammed   +2 more
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Hyperstability of Control Systems [PDF]

Journal of Dynamic Systems, Measurement, and Control, 1974
V. M. Popov, M. R. Posehn
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Dois algoritmos de identificação paramétrica com eliminação de perturbação determinística [PDF]

, 1986
Dissertação (mestrado) - Universidade Federal de Santa Catarina, Centro Tecnológico.
Catelan Neto, Eugênio de Bona
core  

A fixed point approach to the hyperstability of the general linear equation in β-Banach spaces

, 2018
The purpose of this paper is first to reformulate the fixed point theorem (see Theorem 1 of [J. Brzdȩk, J. Chudziak and Z. Páles, A fixed point approach to stability of functional equations, Nonlinear Anal. 74 2011, 17, 6728–6732]) in β-Banach spaces. We
Iz-iddine EL-Fassi, Samir Kabbaj, Abdellatif Chahbi   +2 more
core   +1 more source