scholarly journals Generalized Stability of Euler-Lagrange Quadratic Functional Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Hark-Mahn Kim ◽  
Min-Young Kim
Keyword(s):  
Banach Space ◽  
Functional Equation ◽  
General Solution ◽  
Rational Numbers ◽  
Stability Theorem ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Ulam Stability ◽  
Generalized Stability

The main goal of this paper is the investigation of the general solution and the generalized Hyers-Ulam stability theorem of the following Euler-Lagrange type quadratic functional equationf(ax+by)+af(x-by)=(a+1)b2f(y)+a(a+1)f(x), in(β,p)-Banach space, wherea,bare fixed rational numbers such thata≠-1,0andb≠0.

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

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Abasalt Bodaghi ◽  
Sang Og Kim
Keyword(s):  
Functional Equation ◽  
Positive Integer ◽  
General Solution ◽  
Functional Equations ◽  
Quadratic Functional Equation ◽  
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 Quadratic Functional Equation in Fuzzy Banach Space

2013 ◽  
Vol 373-375 ◽  
pp. 1881-1884
Author(s):  
Xiao Jing Zhan ◽  
Pei Sheng Ji
Keyword(s):  
Banach Space ◽  
Functional Equation ◽  
Fixed Point ◽  
Fixed Point Method ◽  
Point Method ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Ulam Stability ◽  
Fuzzy Banach Space

In this paper, we investigate the Hyers-Ulam stability of the functional equation ƒ(2x+y)+ƒ(2x-y)=8ƒ(x)+2ƒ(y) in fuzzy Banach space using the fixed point method.

scholarly journals A New Approach to Hyers-Ulam Stability of r -Variable Quadratic Functional Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Vediyappan Govindan ◽  
Porpattama Hammachukiattikul ◽  
Grienggrai Rajchakit ◽  
Nallappan Gunasekaran ◽  
R. Vadivel
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
General Solution ◽  
Functional Equations ◽  
Fixed Point Method ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Quadratic Mapping ◽  
Ulam Stability ◽  
New Approach

In this paper, we investigate the general solution of a new quadratic functional equation of the form ∑ 1 ≤ i < j < k ≤ r ϕ l i + l j + l k = r − 2 ∑ i = 1 , i ≠ j r ϕ l i + l j + − r 2 + 3 r − 2 / 2 ∑ i = 1 r ϕ l i . We prove that a function admits, in appropriate conditions, a unique quadratic mapping satisfying the corresponding functional equation. Finally, we discuss the Ulam stability of that functional equation by using the directed method and fixed-point method, respectively.

scholarly journals General solution and generalized Ulam-Hyers stability of a generalized n- type additive quadratic functional equation in Banach space and Banach algebra: direct and fixed point methods

2015 ◽  
Vol 3 (1) ◽  
pp. 25
Author(s):  
S. Murthy ◽  
M. Arunkumar ◽  
V. Govindan
Keyword(s):  
Banach Space ◽  
Functional Equation ◽  
Fixed Point ◽  
Positive Integer ◽  
General Solution ◽  
Banach Algebra ◽  
Banach Algebras ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Fixed Point Methods

<p>In this paper, the authors introduce and investigate the general solution and generalized Ulam-Hyers stability of a generalized <em>n</em>-type additive-quadratic functional equation.</p><p><br />g(x + 2y; u + 2v) + g(x 􀀀 2y; u 􀀀 2v) = 4[g(x + y; u + v) + g(x 􀀀 y; u 􀀀 v)] 􀀀 6g(x; u)<br />+ g(2y; 2v) + g(􀀀2y;􀀀2v) 􀀀 4g(y; v) 􀀀 4g(􀀀y;􀀀v)</p><p>Where  is a positive integer with , in Banach Space and Banach Algebras using direct and fixed point methods.</p>

On the Hyers–Ulam stability and hyperstability of a generalized quadratic functional equation in n-Banach spaces

2021 ◽  
pp. 2250013
Author(s):  
Nordine Bounader
Keyword(s):  
Banach Space ◽  
Functional Equation ◽  
Abelian Group ◽  
Banach Spaces ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Ulam Stability ◽  
Class Of Functions

In this paper, we establish some Hyers–Ulam stability and hyperstability results of the following functional equation [Formula: see text] in the class of functions from an abelian group [Formula: see text] into a [Formula: see text]-Banach space.

Solution and fuzzy stability of a mixed type functional equation

2015 ◽  
Vol 0 (0) ◽  
Author(s):  
P. Narasimman
Keyword(s):  
Functional Equation ◽  
General Solution ◽  
Mixed Type ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Ulam Stability

AbstractIn this paper, we obtain the general solution and we study the generalized Hyers–Ulam stability of the mixed type additive-quadratic functional equation

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

2018 ◽  
Vol 51 (1) ◽  
pp. 295-303
Author(s):  
Gwang Hui Kim ◽  
Iz-iddine El-Fassi ◽  
Choonkil Park
Keyword(s):  
Banach Space ◽  
Functional Equation ◽  
Quadratic Functional Equation ◽  
Inner Product ◽  
Quadratic Functional ◽  
Ulam Stability ◽  
Product Spaces ◽  
Inner Product Spaces ◽  
Class Of Functions

AbstractWe have proved theHyers-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.

GENERALIZED HYERS–ULAM STABILITIES OF AN EULER–LAGRANGE–RASSIAS QUADRATIC FUNCTIONAL EQUATION

2012 ◽  
Vol 05 (01) ◽  
pp. 1250014 ◽  
Author(s):  
A. Zivari-Kazempour ◽  
M. Eshaghi Gordji
Keyword(s):  
Functional Equation ◽  
General Solution ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Ulam Stability

In this paper, we give the general solution of the Euler–Lagrange–Rassias-type quadratic functional equation [Formula: see text] and investigate its generalized Hyers–Ulam stability.

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