TITLE

On the Generalized Hyers-Ulam-Rassias Stability of Quadratic Functional Equations

AUTHOR(S)
Gordji, M. Eshaghi; Khodaei, H.
PUB. DATE
January 2009
SOURCE
Abstract & Applied Analysis;2009, Special section p1
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
We achieve the general solution and the generalized Hyers-Ulam-Rassias and Ulam-Gavruta- Rassias stabilities for quadratic functional equations f(ax + by) + f(ax − by) = (b(a + b)/2)f(x + y) + (b(a + b)/2)f(x − y) + (2a2 − ab − b2)f(x) + (b2 − ab)f(y) where a, b are nonzero fixed integers with b≠ ±a, −3a, and f(ax-by)=f(ax−by) = 2a2f(x)+2b2f(y) for fixed integers a, b with a, b≠ 0 and a ± b ≠ 0.
ACCESSION #
55252846

 

Related Articles

  • GENERALIZED DERIVATIONS AND ITS STABILITY. Sheon-Young Kang; Ick-Soon Chang // Journal of Computational Analysis & Applications;Jul2010, Vol. 12 Issue 3, p593 

    In this article, we are going to examine the generalized Hyers-UIam stability and the superstability of generalized derivations corresponding to the Jensen type functional equation.

  • On Approximate Cubic Homomorphisms. Gordji, M. Eshaghi; Savadkouhi, M. Bavand // Advances in Difference Equations;2009, Special section p1 

    We investigate the generalized Hyers-Ulam-Rassias stability of the system of functional equations: f(xy) = f(x)f(y), f(2x + y) + f(2x - y) = 2f(x + y) + 2f(x - y) + 12f(x), on Banach algebras. Indeed we establish the superstability of this system by suitable control functions.

  • Generalized Hyers-Ulam Stability of Generalized (N,K)-Derivations. Gordji, M. Eshaghi; Rassias, J. M.; Ghobadipour, N. // Abstract & Applied Analysis;2009, Special section p1 

    Let 3 ≤ n, and 3 ≤ k ≤ n be positive integers. Let A be an algebra and let X be an Abimodule. A C-linear mapping d : A → X is called a generalized (n, k)-derivation if there exists a (k − 1)-derivation δ : A → X such that d(a1a2 · · · an) =...

  • Solutions and Stability of Generalized Mixed Type QC Functional Equations in Random Normed Spaces. Yeol Je Cho; Madjid Eshaghi Gordji; Zolfaghari, Somaye // Journal of Inequalities & Applications;2010, Vol. 2010, p1 

    We achieve the general solution and the generalized stability result for the following functional equation in random normed spaces (in the sense of Sherstnev) under arbitrary t-norms: f(x + ky) + f(x - ky) = k2[f(x + y) + f(x - y)] + (2(k2 - 1)/k2(k - 2))f(kx) - ((k3 - k2 - k + 1)/2(k - 2))f(2x)...

  • Non-linear perturbations of homomorphisms on C(X). Semrl, P // Quarterly Journal of Mathematics;Mar1999, Vol. 50 Issue 197, p87 

    Discusses the non-linear mathematical solutions to homomorphisms. Development of a stability theory for linear multiplicative maps under additional boundedness; Cases not needing additional boundedness condition; Theorems used as basis for the perturbations developed.

  • The reduction square root and perturbation for a class of strongly continuous operator families. Chen, Chuang; Song, Xiao; Li, Hui // Acta Mathematica Sinica;Oct2010, Vol. 26 Issue 10, p1993 

    We introduce the concept of α times C-second resolvent families and present the relationship between α times C-resolvent families and α times C-second resolvent families. Moreover, the perturbation and square root for α times C-resolvent families are considered in this paper which...

  • A METHOD OF FINDING AN INTEGRAL SOLUTION TO x3+y3 = kz4. Zahari, N. M.; Sapar, S. H.; Mohd. Atan, K. A. // AIP Conference Proceedings;11/11/2010, Vol. 1309 Issue 1, p842 

    In this article, we proved that an integral solution (a, b, c) to the equation x3+y3 = kz4 is of the form a = rs, b = rt for any two integers s, t and c = (r3ud3)1/4 for some u with (k,r) = d where k divides a3+b3 and r is a common factor of a and b.

  • Simulation of 3-D Teleseismic SV-waves Accelerated by the Multilevel Fast Multipole Method. Çakir, Özcan // Pure & Applied Geophysics;Sep2008, Vol. 165 Issue 9/10, p1707 

    We use first-order perturbation theory to represent the three-dimensional (3-D) seismic structure of the Earth. The background structure is assumed one-dimensional (1-D) with variations in only vertical direction. The perturbations are assumed 3-D volumetric inclusions with certain velocity...

  • Magnetic fluid labyrinthine instability in Hele-Shaw cell with time dependent gap. Tatulchenkov, A.; Cebers, A. // Physics of Fluids;May2008, Vol. 20 Issue 5, p054101 

    The free surface instability of a magnetic fluid in the Hele-Shaw cell with a time dependent gap is theoretically and numerically studied. The numerical algorithm is based on the boundary integral equation technique previously developed. Numerical results illustrate the role of magnetic forces...

Share

Read the Article

Courtesy of VIRGINIA BEACH PUBLIC LIBRARY AND SYSTEM

Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics