Results 301 to 310 of about 456,013 (364)
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Quadratic Operators and Quadratic Functional Equation
2012In 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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Conditional equations for quadratic functions
Acta Mathematica Hungarica, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Boros, Z., Garda-Mátyás, E.
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Quadratic Functional Equations
2009Quadratic 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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Quadratic Functional Equations
2011So far, we have discussed the stability problems of functional equations in connection with additive or linear functions. In this chapter, the Hyers–Ulam–Rassias stability of quadratic functional equations will be proved. Most mathematicians may be interested in the study of the quadratic functional equation since the quadratic functions are applied to
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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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