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Neutral Autonomous Functional Equations with Quadratic Cost
SIAM Journal on Control, 1974In this paper a control problem for neutral functional equations with a quadratic cost function is considered. It is shown that the optimal control is a feedback control. If the problem can be optimized over the positive half-line, then the solution of the problem is obtained by solving a linear homogeneous functional equation which possesses a type of
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Quadratic Functional Equation and Inner Product Spaces
Results in Mathematics, 1995The aim of the paper is to characterize inner product spaces as those in which the square of the norm satisfies some functional equations. The author considers five such equations. Actually, the equations are solved in general, and in some important cases it is noticed that their only solutions are quadratic functionals (i.e. functionals satisfying the
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Quadratic functions satisfying an additional equation
Acta Mathematica Hungarica, 2020The author studies the quadratic functions \(f\) which satisfy \[f(x)=\delta x^{4}f \left(\frac{1}{x}\right),\; x\in \mathbb{R}^* \] and determine all the quadratic solutions of the above equation, where \(\delta =1\) or \(\delta =-1\) and \(\mathbb{R}^{*}=\mathbb{R}\setminus \{0\} .\) Specifically, the author derives and proves that if \(f:\mathbb{R ...
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Quadratic variation functionals and dilation equations
Potential Analysis, 1995zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gundy, Richard F., Iribarren, Ileana
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The quadratic functional equation on groups
Publicationes Mathematicae Debrecen, 2005The quadratic functional equation \[ f(xy)+f(xy^{-1})=2f(x)+2f(y) \] is considered on free groups. The author presents the result on a general solution of the above equation defined on a free group with values in an abelian group. In the proof some results concerning the Jensen functional equation are utilized.
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Set valued pexiderized quadratic functional equation
Aequationes mathematicaezbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mohammadi, Elham +2 more
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Stability of the Quadratic Functional Equation
1998The quadratic functional equation $$ f\left( {x + y} \right) + f\left( {x - y} \right) - 2f\left( x \right) - 2f\left( y \right) = 0$$ (3.1) clearly has f(x) = cx2 as a solution with c an arbitrary constant when f is a real function of a real variable.
Donald H. Hyers +2 more
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Stability of a Quadratic Functional Equation
Advances in Dynamical Systems and Applications, 2021S. Jaikumar +4 more
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