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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 Transformations of Appell Functions
SIAM Journal on Mathematical Analysis, 1976A double integral average of x/sup t/ with two rows and two columns has eight quadratic transformations into itself, each with two free parameters and two independent variables. Three of the transformations change double hypergeometric series of order two into series of order three, and one of these (modified by a linear transformation applicable to ...
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Iterative minimization of quadratic functional
Circuits Systems and Signal Processing, 1995The author considers the gradient algorithm for minimizing convex continuous quadratic functionals in Hilbert spaces. He shows that the algorithm with fixed stepsize converges whenever the stepsize is small enough, and motivates his result by some filtering problems that occur in the theory of discrete time systems.
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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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IEEE Transactions on Neural Networks and Learning Systems, 2022
Jun Chen, Xian-Ming Zhang, Ju H. Park
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Jun Chen, Xian-Ming Zhang, Ju H. Park
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A relaxed quadratic function negative-determination lemma and its application to time-delay systems
Automatica, 2020Chuan-Ke Zhang, Fei Long, Yong He
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