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Stability of an additive-quadratic-quartic functional equation

Kim Gwang Hui, Lee Yang-Hi

Demonstratio Mathematica

2020

Vol. 53, nr 1

1--7

In this paper, we investigate the stability of an additive-quadratic-quartic functional equation f(x+2y)+f(x-2y) - 2f(x+y) - 2f(-x-y) - 2f(x-y) - 2f(y-x)+4f(-x)+2f(x) - f(2y) - f(-2y)+4f(y)+4f(-y)=0 by the direct method in the sense of Găvruta.

Stability and hyperstability of a quadratic functional equation and a characterization of inner product spaces

EL-Fassi I., Park C., Kim G. H.

Demonstratio Mathematica

2018

Vol. 51, nr 1

295--303

We have proved the Hyers-Ulam stability and the hyperstability of the quadratic functional equation f(x+y+z) +f(x+y−z) +f(x−y+z) +f(−x+y+z) = 4[f(x) +f(y) +f(z) ] in the class of functions from an abelian group G into a Banach space.

Note on the stability of the system of functional equations

Adam M.

Silesian Journal of Pure and Applied Mathematics

2017

Vol. 7, iss. 1

93--98

We deal with the system of functional equations connected with additive and quadratic mappings. We correct some mistakes made in the paper [W. Fechner, On the Hyers-Ulam stability of functional equations connected with additive and quadratic mappings, J. Math. Anal. Appl. 322 (2006), 774–786] and provide accurate statements of those results. Moreover, we get the improvement of the Hyers-Ulam stability result of the considered system of functional equations.

On the equation of the p-orthogonal additivity

Alsina C., Sikorska J., Tomas M.S.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2007

Vol. 47, [Z] 2

171-178

We solve a conditional functional equation of the form x ⊥y ⇒ f(x + y) = f(x) + f(y), where f is a mapping from a real normed linear space (X, k ź k) with dimX ≥2 into an abelian group (G, +) and ⊥ is a given orthogonality relation associated to the norm.

The stability of the quadratic equation for set valued mappings

Czerwik S., Dłutek K.

Zeszyty Naukowe. Matematyka - Fizyka / Politechnika Śląska

1999

z. 84

105-116

In the paper we consider the problem of the Ulam-Hyers and Rassias types of stability of the quadratic functional equation for set-valued functions.

W artykule rozpatrywany jest problem stabilności równania funkcjonałów kwadratowych dla funkcji wielowartościowych.

On inner product spaces - III

Kannapann P.

Bulletin of the Polish Academy of Sciences. Mathematics

1998

Vol. 46, no 1

1-4

When one deals with normed linear space (n.l.s.), the natural question arises when a n.l.s. is an inner product space (i.p.s.)? What further conditions the norm has to satisfy so that the n.l.s. an inner product space? Numerous charakterizations are known [2, 1, 2, 4, 5, 6, 7]. In this paper we study i.p.s. from functional equations point of view and consider three functional equations (ME), (14) and (15) which are generalizations of (LE) found in [6].