Fuzzy Stability of Quadratic Functional Equations in General Cases

Quadratic Functional ◽

The aim of this paper is to investigate fuzzy Hyers-Ulam-Rassias stability of the general case of quadratic functional equation where and fixed integers with . These functional equations are equivalent. This has been proven by Ulam, 1964.

On the generalized orthogonal stability of the pexiderized quadratic functional equations in modular spaces

Mathematica Slovaca ◽

10.1515/ms-2016-0255 ◽

2017 ◽

Vol 67 (1) ◽

Cited By ~ 4

Author(s):

Iz-iddine EL-Fassi ◽

Samir Kabbaj

Keyword(s):

Functional Equation ◽

Functional Equations ◽

Quadratic Functional ◽

Modular Spaces ◽

Generalized Orthogonal ◽

AbstractIn this paper, we establish the Hyers-Ulam-Rassias stability of the quadratic functional equation of Pexiderized type

On the Stability of Quadratic Functional Equations inF-Spaces

Journal of Function Spaces ◽

10.1155/2016/5636101 ◽

2016 ◽

Vol 2016 ◽

pp. 1-7 ◽

Cited By ~ 1

Author(s):

Xiuzhong Yang

Keyword(s):

Functional Equation ◽

Functional Equations ◽

Quadratic Functional ◽

The Stability ◽

The Hyers-Ulam-Rassias stability of quadratic functional equationf(2x+y)+f(2x-y)=f(x+y)+f(x-y)+6f(x)and orthogonal stability of the Pexiderized quadratic functional equationf(x+y)+f(x-y)=2g(x)+2h(y)inF-spaces are proved.

Stability for the Mixed Type of Quartic and Quadratic Functional Equations

Journal of Function Spaces ◽

10.1155/2014/853743 ◽

2014 ◽

Vol 2014 ◽

pp. 1-10

Author(s):

Young-Su Lee ◽

Soomin Kim ◽

Chaewon Kim

Keyword(s):

Functional Equation ◽

Functional Equations ◽

Mixed Type ◽

Quadratic Functional ◽

General Solutions ◽

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). Moreover we prove the Hyers-Ulam-Rassias stability of this equation under the approximately quartic and the approximately quadratic conditions.

On alienation of two functional equations of quadratic type

Aequationes Mathematicae ◽

10.1007/s00010-021-00809-7 ◽

2021 ◽

Author(s):

Roman Ger

Keyword(s):

Functional Equation ◽

Functional Equations ◽

Quadratic Functional ◽

Real Numbers ◽

Alpha Beta ◽

Beta 2 ◽

Special Case

Abstract We deal with an alienation problem for an Euler–Lagrange type functional equation $$\begin{aligned} f(\alpha x + \beta y) + f(\alpha x - \beta y) = 2\alpha ^2f(x) + 2\beta ^2f(y) \end{aligned}$$ f ( α x + β y ) + f ( α x - β y ) = 2 α 2 f ( x ) + 2 β 2 f ( y ) assumed for fixed nonzero real numbers $$\alpha ,\beta ,\, 1 \ne \alpha ^2 \ne \beta ^2$$ α , β , 1 ≠ α 2 ≠ β 2 , and the classic quadratic functional equation $$\begin{aligned} g(x+y) + g(x-y) = 2g(x) + 2g(y). \end{aligned}$$ g ( x + y ) + g ( x - y ) = 2 g ( x ) + 2 g ( y ) . We were inspired by papers of Kim et al. (Abstract and applied analysis, vol. 2013, Hindawi Publishing Corporation, 2013) and Gordji and Khodaei (Abstract and applied analysis, vol. 2009, Hindawi Publishing Corporation, 2009), where the special case $$g = \gamma f$$ g = γ f was examined.

Projective actions, invariant sigma-curves and quadratic functional equations

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100063416 ◽

1985 ◽

Vol 98 (2) ◽

pp. 195-212 ◽

Cited By ~ 1

Author(s):

Patrick J. McCarthy

Keyword(s):

Functional Equation ◽

Periodic Function ◽

Functional Equations ◽

Continuous Solution ◽

Quadratic Functional ◽

Continuous Solutions ◽

Linear Map

AbstractThe quadratic functional equation f(f(x)) *–Tf(x) + Dx = 0 is equivalent to the requirement that the graph be invariant under a certain linear map The induced projective map is used to show that the equation admits a rich supply of continuous solutions only when L is hyperbolic (T2 > 4D), and then only when T and D satisfy certain further conditions. The general continuous solution of the equation is given explicitly in terms of either (a) an expression involving an arbitrary periodic function, function additions, inverses and composites, or(b) suitable limits of such solutions.

HYERS-ULAM-RASSIAS STABILITY OF A QUADRATIC FUNCTIONAL EQUATION

Bulletin of the Korean Mathematical Society ◽

10.4134/bkms.2003.40.2.253 ◽

2003 ◽

Vol 40 (2) ◽

pp. 253-267 ◽

Cited By ~ 5

Author(s):

Tiberiu Trif

Keyword(s):

Functional Equation ◽

Quadratic Functional ◽

Stability of a Functional Equation Deriving from Quadratic and Additive Functions in Non-Archimedean Normed Spaces

Abstract and Applied Analysis ◽

10.1155/2013/198018 ◽

2013 ◽

Vol 2013 ◽

pp. 1-10 ◽

Cited By ~ 2

Author(s):

Abasalt Bodaghi ◽

Sang Og Kim

Keyword(s):

Functional Equation ◽

Positive Integer ◽

General Solution ◽

Functional Equations ◽

Quadratic Functional ◽

Ulam Stability ◽

Additive Functions ◽

Normed Spaces

We obtain the general solution of the generalized mixed additive and quadratic functional equationfx+my+fx−my=2fx−2m2fy+m2f2y,mis even;fx+y+fx−y−2m2−1fy+m2−1f2y,mis odd, for a positive integerm. We establish the Hyers-Ulam stability for these functional equations in non-Archimedean normed spaces whenmis an even positive integer orm=3.

Stability of Generalized Quadratic Functional Equation in Non-Archimedean Fuzzy Normed Spaces

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.403-408.879 ◽

2011 ◽

Vol 403-408 ◽

pp. 879-887

Author(s):

K. Ravi ◽

P. Narasimman

Keyword(s):

Functional Equation ◽

General Solution ◽

Quadratic Functional ◽

Normed Spaces ◽

In this paper, we obtain the general solution and investigate the Hyers-Ulam-Rassias stability of the Generalized Quadratic functional equation in non-Archimedean fuzzy normed spaces.