• Nonlinear Functional Analysis and Applications
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• 제28권4호
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• pp.865-876
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• 2023

This paper presents properties of the cocycle equations via cochains on a semigroup. And then we offer hyperstability results of related functional equations using the properties of cocycle equations via cochains. These results generalize hyperstability results of a class of linear functional equation by Maksa and Páles. The obtained results can be applied to obtain hyperstability of various functional equations such as Euler-Lagrange type quadratic equations.

• 대한전자공학회논문지
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• 제25권5호
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• pp.482-489
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• 1988

In this paper, we proposed a generalized model reference adaptive control theory which can be applied to single-input single-output discrete system by using V.M.Popov's hyperstability theory. As the result of theoretical analysis, it is proved that the discrete adaptive control scheme proposed by Narendra is a special case of the adaptive control schemes proposed in this paper. Also we suggest a variety of parameter adaptiations methods of controller through hyperstability theory.

• 대한수학회보
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• 제52권6호
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• pp.1827-1838
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• 2015

We give some results on hyperstability for the general linear equation. Namely, we show that a function satisfying the linear equation approximately (in some sense) must be actually the solution of it.

• 충청수학회지
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• 제36권2호
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• pp.107-123
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• 2023

In this paper, we present some hyperstability results for a general quintic functional equation and a general septic functional equation.

• 대한수학회논문집
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• 제33권3호
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• pp.901-917
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• 2018

In this paper, we first introduce the notions of (2, ${\beta}$)-Banach spaces and we will reformulate the fixed point theorem [10, Theorem 1] in this space. We also show that this theorem is a very efficient and convenient tool for proving the new hyperstability results of the general linear equation in (2, ${\beta}$)-Banach spaces. Our main results state that, under some weak natural assumptions, functions satisfying the equation approximately (in some sense) must be actually solutions to it. Our results are improvements and generalizations of the main results of Piszczek [34], Brzdęk [6, 7] and Bahyrycz et al. [2] in (2, ${\beta}$)-Banach spaces.

• 충청수학회지
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• 제33권1호
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• pp.147-156
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• 2020

The functional equation related to a distance measure f(pr, qs) + f(ps, qr) = M(r, s)f(p, q) + M(p, q)f(r, s) can be generalized a sum form functional equation as follows $${\frac{1}{n}}{\sum\limits_{i=0}^{n-1}}f(P{\cdot}{\sigma}_i(Q))=M(Q)f(P)+M(P)f(Q)$$ where f, g is information measures, P and Q are the set of n-array discrete measure, and σ_i is a permutation for each i = 0, 1, ⋯, n-1. In this paper, we obtain the hyperstability of the above type functional equation.

• 대한수학회논문집
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• 제36권2호
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• pp.343-359
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• 2021

The aim of this paper is to obtain the general solution of the 2-variable radical functional equations $f({\sqrt[k]{x^k+z^k}},\;{\sqrt[{\ell}]{y^{\ell}+w^{\ell}}})=f(x,y)+f(z,w)$, x, y, z, w ∈ ℝ, for f a mapping from the set of all real numbers ℝ into a vector space, where k and ℓ are fixed positive integers. Also using the fixed point result of Brzdęk and Ciepliński [11, Theorem 1] in (2, 𝛽)-Banach spaces, we prove the generalized hyperstability results of the 2-variable radical functional equations. In the end of this paper we derive some consequences from our main results.

• 호남수학학술지
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• 제42권2호
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• pp.391-409
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• 2020

In the current paper, the intuitionistic fuzzy normed space version of Hyers-Ulam stability for multi-additive, multi-cubic and multi-additive-cubic mappings by using a fixed point method are studied. Moreover, a few corollaries corresponding to some known stability and hyperstability outcomes in intuitionistic fuzzy normed space are presented.

• Journal of applied mathematics & informatics
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• 제41권3호
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• pp.469-485
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• 2023

In this paper, we investigate the Hyers-Ulam-Rassias stability for a Drygas functional equation g(u + v) + g(u - v) = 2g(u) + g(v) + g(-v) in the setting of quasi-Banach space using fixed point approach. Also, we give general results on hyperstability of a Drygas functional equation. The results obtain in this paper extend various previously known results in the setting of quasi-Banach space. Some examples are also illustrated.

• 조명전기설비학회논문지
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• 제21권10호
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• pp.73-81
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• 2007

서보 모터의 순시 토크 제어 능력의 개선을 위해 PMSM 서보 모터의 적응형 전류 제어기 설계 방법을 제안한다. 동기좌표 전류 제어기에서 비결합 제어 입력을 이용하여 새로운 제어 입력 항을 얻을 수 있으며 이를 통해 제어기의 원하는 대역폭을 선정할 수 있지만 모터의 파라미터 변화, 데드타임에 의한 인버터의 왜곡 등의 외란에 의해 제어 성능이 저하된다. 이러한 단점을 개선하기 위해 PMSM 서보 모터의 적응형 전류 제어기의 설계 방법을 제안하며 설계 방법이 초안정(hyperstability) 이론에 의해 구해진다. 제안된 제어 방식의 점근안정성을 이론적으로 증명하고 DSP TMS320C31을 이용한 시뮬레이션과 실험을 통해 입증한다.