On the stability of Drygas functional equation on groups

Faiziev, V. A.; Sahoo, Prasanna K.

doi:10.15352/bjma/1240321554

Cited by 10 publications

(11 citation statements)

References 14 publications

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“…The stability of the Drygas functional equation has been studied by many authors under various conditions (see, for example, [9][10][11]15] and references therein). In 2013, results on the hyperstability of the Drygas functional equation were obtained by Piszczek and Szczawińska [14].…”

Section: Introductionmentioning

confidence: 99%

Two New Generalised Hyperstability Results for the Drygas Functional Equation

Aiemsomboon¹,

Sintunavarat²

2017

Bull. Aust. Math. Soc.

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Let $X$ be a nonempty subset of a normed space such that $0\notin X$ and $X$ is symmetric with respect to $0$ and let $Y$ be a Banach space. We study the generalised hyperstability of the Drygas functional equation $$\begin{eqnarray}f(x+y)+f(x-y)=2f(x)+f(y)+f(-y),\end{eqnarray}$$ where $f$ maps $X$ into $Y$ and $x,y\in X$ with $x+y,x-y\in X$. Our first main result improves the results of Piszczek and Szczawińska [‘Hyperstability of the Drygas functional equation’, J. Funct. Space Appl.2013 (2013), Article ID 912718, 4 pages]. Hyperstability results for the inhomogeneous Drygas functional equation can be derived from our results.

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Section: Introductionmentioning

confidence: 99%

Two New Generalised Hyperstability Results for the Drygas Functional Equation

Aiemsomboon¹,

Sintunavarat²

2017

Bull. Aust. Math. Soc.

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“…The solutions of Drygas equation in abelian group are obtained by Stetkaer in [24]. Various authors studied the Drygas equation, for example Ebanks et al [10], Faȋziev and Sahoo [11], Jung and Sahoo [17], Ã Lukasik [18], Szabo [26],Yang [27].…”

Section: Introductionmentioning

confidence: 99%

“…There are several functional equations reduced to those of the Drygas functional equation (1.1), i.e. the mixed type additive, quadratic, Jensen and Pexidered equations, we refer, for example, to [1], [2], [4]- [8], [11]- [16], [19].…”

Section: Introductionmentioning

confidence: 99%

A generalization of Drygas functional equation

Charifi

Almahalebi

Kabbaj

2016

Proyecciones (Antofagasta)

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“…The functional equation (1.3) has been studied by Gy. Szabo [22], B. R. Ebanks et al [6], V. A. Faȋziev and P. K. Sahoo [8]. The solutions of equation (1.3) in abelian group are obtained by H. Stetkaer in [21].…”

Section: Introductionmentioning

confidence: 99%