scholarly journals Generalized Stability ofC*-Ternary Quadratic Mappings

2007 ◽  
Vol 2007 ◽  
pp. 1-6 ◽  
Author(s):  
Choonkil Park ◽  
Jianlian Cui
Keyword(s):  
Functional Equation ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Quadratic Mappings ◽  
Generalized Stability

We prove the generalized stability ofC*-ternary quadratic mappings inC*-ternary rings for the quadratic functional equationf(x+y)+f(x−y)=2f(x)+2f(y).

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 Ulam Type Stability of ?-Quadratic Mappings in Fuzzy Modular ∗-Algebras

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1630
Author(s):  
Hark-Mahn Kim ◽  
Hwan-Yong Shin
Keyword(s):  
Functional Equation ◽  
Lower Semicontinuity ◽  
Product Space ◽  
Quadratic Functional Equation ◽  
Inner Product ◽  
Quadratic Functional ◽  
Quadratic Mappings ◽  
The Stability ◽  
Ulam Type Stability ◽  
Stability Results

In this paper, we find the solution of the following quadratic functional equation n∑1≤i<j≤nQxi−xj=∑i=1nQ∑j≠ixj−(n−1)xi, which is derived from the gravity of the n distinct vectors x1,⋯,xn in an inner product space, and prove that the stability results of the A-quadratic mappings in μ-complete convex fuzzy modular ∗-algebras without using lower semicontinuity and β-homogeneous property.

scholarly journals Nearly Quadratic Mappings overp-Adic Fields

2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
M. Eshaghi Gordji ◽  
H. Khodaei ◽  
Gwang Hui Kim
Keyword(s):  
Functional Equation ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Quadratic Mappings ◽  
Stability Results

We establish some stability results overp-adic fields for the generalized quadratic functional equation∑k=2n∑i1=2k∑i2=i1+1k+1⋯∑in-k+1=in-k+1nf(∑i=1,i≠i1,…,in-k+1nxi-∑r=1n-k+1xir)+f(∑i=1nxi)=2n-1∑i=1nf(xi),wheren∈Nandn≥2.

scholarly journals On alienation of two functional equations of quadratic type

2021 ◽  
Author(s):  
Roman Ger
Keyword(s):  
Functional Equation ◽  
Functional Equations ◽  
Quadratic Functional Equation ◽  
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

1985 ◽  
Vol 98 (2) ◽  
pp. 195-212 ◽  
Author(s):  
Patrick J. McCarthy
Keyword(s):  
Functional Equation ◽  
Periodic Function ◽  
Functional Equations ◽  
Continuous Solution ◽  
Quadratic Functional Equation ◽  
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.

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