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Stability of a Quartic Functional Equation [PDF]

The Scientific World Journal, 2014
We obtain the general solution of the generalized quartic functional equation f(x+my)+f(x-my)=2(7m-9)(m-1)f(x)+2m2(m2-1)f(y)-(m-1)2f(2x)+m2{f(x+y) + f(x-y)} for a fixed positive integer m.
Abasalt Bodaghi
doaj   +6 more sources

The Stability Analysis of A-Quartic Functional Equation [PDF]

Mathematics, 2021
In this paper, we study the general solution of the functional equation, which is derived from additive–quartic mappings. In addition, we establish the generalized Hyers–Ulam stability of the additive–quartic functional equation in Banach spaces by using
Chinnaappu Muthamilarasi, Shyam Sundar Santra, Ganapathy Balasubramanian, Vediyappan Govindan, Rami Ahmad El-Nabulsi, Khaled Mohamed Khedher   +5 more
doaj   +5 more sources

Fuzzy Stability Results of Generalized Quartic Functional Equations [PDF]

Mathematics, 2021
In the present paper, we introduce a new type of quartic functional equation and examine the Hyers–Ulam stability in fuzzy normed spaces by employing the direct method and fixed point techniques.
Sang Og Kim, Kandhasamy Tamilvanan
doaj   +5 more sources

Ulam Stability of a Quartic Functional Equation [PDF]

Abstract and Applied Analysis, 2012
The oldest quartic functional equation was introduced by J. M. Rassias in (1999), and then was employed by other authors. The functional equation 𝑓(2𝑥+𝑦)+𝑓(2𝑥−𝑦)=4𝑓(𝑥+𝑦)+4𝑓(𝑥−𝑦)+24𝑓(𝑥)−6𝑓(𝑦) is called a quartic functional equation, all of its solution is
Abasalt Bodaghi, Idham Arif Alias, Mohammad Hosein Ghahramani   +2 more
doaj   +8 more sources

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   +4 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   +4 more sources

Stability for the Mixed Type of Quartic and Quadratic Functional Equations [PDF]

Journal of Function Spaces, 2014
We establish the general solutions of the following mixed type of quartic and quadratic functional equation: f(2x+y)+f(2x-y)=4f(x+y)+4f(x-y)+2f(2x)-8f(x)-6f(y).
Young-Su Lee, Soomin Kim, Chaewon Kim
doaj   +7 more sources

Fuzzy Stability of an Additive-Quadratic-Quartic Functional Equation [PDF]

Journal of Inequalities and Applications, 2010
Using the fixed point method, we prove the generalized Hyers-Ulam stability of the following additive-quadratic-quartic functional equation: in fuzzy Banach spaces.
Park Choonkil
doaj   +18 more sources

Stability of a Quartic Functional Equation in Restricted Domains [PDF]

Journal of Function Spaces, 2016
Let X be a real normed space and Y a Banach space and f:X→Y. We prove the Ulam-Hyers stability theorem for the quartic functional equation f(2x+y)+f(2x-y)-4f(x+y)-4f(x-y)-24f(x)+6f(y)=0 in restricted domains.
Jaeyoung Chung, Yu-Min Ju
doaj   +7 more sources

ON THE GENERAL SOLUTION OF A QUARTIC FUNCTIONAL EQUATION [PDF]

Bulletin of the Korean Mathematical Society, 2003
Using a classical result of M. Hosszú and applying elegant and elementary arguments the authors find the general solution of the functional equation: \[ f(x + 2y) + f(x-2y) + 6 f(x) = 4 (f (x+y) + f(x-y) + 6 f(y)), \] i.e., \( f(x) = A^4 (x)\) which is the diagonal of a 4-additive symmetric function from \(R^4\) into \(R\). By means of some results due
Prasanna K Sahoo
exaly   +2 more sources