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A functional equation originating from quadratic forms [PDF]

Journal of Mathematical Analysis and Applications, 2007
In this paper, we obtain the general solution and the stability of the 2-variable quadratic functional equationf(x+y,z+w)+f(x−y,z−w)=2f(x,z)+2f(y,w).
Won-Gil Park
exaly   +2 more sources

The stability of the quadratic functional equation on amenable groups [PDF]

Journal of Mathematical Analysis and Applications, 2004
All the literature on the stability of the quadratic functional equation focus on the case where the relevant domain is an Abelian group or a normed space.
Dilian Yang
exaly   +2 more sources

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The quadratic function and quadratic equations

1985
The function f(x), where f(x) = ax2 + bx + c, and a, b, c are constants, a ≠ 0, is called a quadratic function, or sometimes a quadratic polynomial. From elementary algebra $${(x + d)^2} \equiv {x^2} + 2dx + {d^2}.$$ Using this, we write $$a{x^2} + bx + c \equiv a\left( {{x^2} + \frac{b}{a}x + \frac{c}{a}} \right) \equiv a\left[ {{{\left( {x
J. E. Hebborn, C. Plumpton
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Set-Valued Quadratic Functional Equations

Results in Mathematics, 2017
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lee, Jung Rye, Park, Choonkil, Shin, Dong Yun, Yun, Sungsik   +3 more
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On the stability of a quadratic Jensen type functional equation [PDF]

Journal of Mathematical Analysis and Applications, 2002
In this paper we obtain the general solution of the quadratic Jensen type functional equation 9fx+y+z3+f(x)+f(y)+f(z)=4fx+y2+fy+z2+fz+x2 and prove the stability of this equation in the spirit of Hyers, Ulam, Rassias, and ...
Lee, Young Whan
exaly   +2 more sources

Quadratic Operators and Quadratic Functional Equation

2012
In the first part of this paper, we consider some quadratic difference operators (e.g., Lobaczewski difference operators) and quadratic-linear difference operators (d’Alembert difference operators and quadratic difference operators) in some special function spaces X λ . We present results about boundedness and find the norms of such operators.
M. Adam, S. Czerwik
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On the connection of the quadratic Lienard equation with an equation for the elliptic functions

Regular and Chaotic Dynamics, 2015
Consider the differential equation \[ {d^2y\over dx^2}+ g(y)\Biggl({dy\over dx}\Biggr)^2+ h(y)= 0.\tag{\(*\)} \] The authors prove that \((*)\) can be transformed into the differential equation \[ w{d^2w\over d\xi^2}-{1\over 2}\Biggl({dw\over d\xi}\Biggr)^2+ 4\omega^3=0\tag{\(**\)} \] by means of the nonlocal transformation \[ w=F(y),\quad d\xi= G(y ...
Kudryashov, Nikolay A., Sinelshchikov, Dmitry I.   +1 more
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Stability of the quadratic functional equation in Lipschitz spaces [PDF]

Journal of Mathematical Analysis and Applications, 2004
Let G be an Abelian group with a metric d and E a normed space. For any f:G→E we define the quadratic difference of the function f by the formula Qf(x,y):=2f(x)+2f(y)−f(x+y)−f(x−y) for x,y∈G.
Dłutek, K., Czerwik, S.
exaly   +2 more sources

Conditional equations for quadratic functions

Acta Mathematica Hungarica, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Boros, Z., Garda-Mátyás, E.
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Quadratic Functional Equations

2009
Quadratic functional equations, bilinear forms equivalent to the quadratic equation, and some generalizations are treated in this chapter. Among the normed linear spaces (n.l.s.), inner product spaces (i.p.s.) play an important role. The interesting question when an n.l.s. is an i.p.s. led to several characterizations of i.p.s.
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