Results 1 to 10 of about 29,994 (153)

General Cubic-Quartic Functional Equation [PDF]

Abstract and Applied Analysis, 2011
We obtain the general solution and the generalized Hyers-Ulam stability of the general cubic-quartic functional equation for fixed integers k with 𝑘≠0,±1: 𝑓(𝑥+𝑘𝑦)+𝑓(𝑥−𝑘𝑦)=𝑘2(𝑓(𝑥+𝑦)+𝑓(𝑥−𝑦))+2(1−𝑘2)𝑓(𝑥)+((𝑘4−𝑘2)/4)(𝑓(2𝑦)−8𝑓(𝑦))+𝑓(2𝑥)−16𝑓(𝑥), where 𝑓(𝑥)∶=
M. Eshaghi Gordji, M. Kamyar, Th. M. Rassias   +2 more
doaj   +3 more sources

Stability of an Additive-Cubic-Quartic Functional Equation [PDF]

Advances in Difference Equations, 2009
In this paper, we consider the additive-cubic-quartic functional equation and prove the generalized Hyers-Ulam stability of the additive-cubic-quartic functional equation in Banach spaces.
Kaboli-Gharetapeh S, Park Choonkil, Eshaghi-Gordji M, Zolfaghari Somayyeh   +3 more
doaj   +3 more sources

Stability of Cubic Functional Equation in the Spaces of Generalized Functions [PDF]

Journal of Inequalities and Applications, 2007
In this paper, we reformulate and prove the Hyers-Ulam-Rassias stability theorem of the cubic functional equation f(ax+y)+f(ax−y)=af(x+y)+af(x−y)+2a(a2−1)f(x) for fixed integer a with a≠0,±1 in the spaces of Schwartz tempered
Soon-Yeong Chung, Young-Su Lee
doaj   +2 more sources

Approximately cubic functional equations and cubic multipliers [PDF]

Journal of Inequalities and Applications, 2011
In this paper, we prove the Hyers-Ulam stability and the superstability for cubic functional equation by using the fixed point alternative theorem. As a consequence, we show that the cubic multipliers are superstable under some conditions.
Alias Idham, Bodaghi Abasalt, Ghahramani Mohammad   +2 more
doaj   +2 more sources

Stability of a Functional Equation Deriving from Cubic and Quartic Functions [PDF]

Abstract and Applied Analysis, 2008
We obtain the general solution and the generalized Ulam‐Hyers stability of the cubic and quartic functional equation 4(f(3x + y) + f(3x − y)) = −12(f(x + y) + f(x − y)) + 12(f(2x + y) + f(2x − y)) − 8f(y)−192f(x) + f(2y) + 30f(2x).
S. Zolfaghari, A. Ebadian, M. Eshaghi Gordji   +2 more
doaj   +5 more sources

Stability for the functional equation of cubic type

Journal of Mathematical Analysis and Applications, 2007
The authors offer a (generalized) Hyers-Ulam [\textit{S. M. Ulam}, Problems in modern mathematics, Wiley, New York (1964; Zbl 0137.24201), Ulam originally posed the problem in 1940; \textit{D. H. Hyers}, Proc. Nat. Acad. Sci. USA. 27, 222--224 (1941; Zbl 0061.26403)] stability result for the functional equation \[ \begin{multlined} f(x_1+x_2+2x_3)+f ...
Ick-Soon Chang, Yong-Soo Jung
exaly   +2 more sources

On the stability of the generalized cubic set-valued functional equation

Applied Mathematics Letters, 2014
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ahyoung Kim, Hahng-Yun Chu
exaly   +3 more sources

Stability Results for Some Classes of Cubic Functional Equations

Axioms
Applications involving functional equations (FUEQs) are commonplace. They are essential to various applications, such as fog computing. Ulam’s notion of stability is highly helpful since it provides a range of estimates between exact and approximate ...
El-sayed El-hady, Yamin Sayyari, Mehdi Dehghanian, Ymnah Alruwaily   +3 more
doaj   +2 more sources

Mittag-Leffler-Hyers-Ulam-Rassias stability of cubic functional equation [PDF]

Mathematics and Computational Sciences, 2021
In this paper, we prove the Mittag-Leffler-Hyers-Ulam-Rassias stability for cubic functional equation by using the fixed point alternative theorem. As a consequence, we show that the cubic multipliers are superstable under some conditions.
V Kalvandi, M. E Samei
doaj   +1 more source

On the Stability of a Cubic Functional Equation in Random Normed Spaces

Journal of Mathematical Extension, 2009
The concept of Hyers-Ulam-Rassias stability has been originated from a stability theorem due to Th. M. Rassias. Recently, the Hyers-Ulam-Rassias stability of the functional equation f(x + 2y) + f(x − 2y) = 2f(x) − f(2x) + 4n f(x + y) + f(x − y) o ,
H. Azadi Kenary
doaj   +2 more sources