Complex Vector Functional Equations
The subject of complex vector functional equations is a new area in the theory of functional equations. This monograph provides a systematic overview of the authors' recently obtained results concerning both linear and nonlinear complex vector functional equations, in all aspects of their utilization. It is intended for mathematicians, physicists and engineers who use functional equations in their investigations. Contents: Linear Complex Vector Functional Equations: General Classes of Cyclic Functional Equations; Functional Equations with Operations Between Arguments; Functional Equations with Constant Parameters; Functional Equations with Constant Coefficients; Systems of Linear Functional Equations; Nonlinear Complex Vector Functional Equations: Quadratic Functional Equations; Modified Quadratic Functional Equations; Expanded Quadratic Functional Equations; Higher Order Functional Equations; Systems of Nonlinear Functional Equations. Readership: Researchers, lecturers, senior undergraduates and graduate students dealing with functional equations.
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According to Eq analytic function arbitrary complex functions arbitrary complex vector arbitrary constant complex arbitrary continuous complex arbitrary functions basis of Eqs complex vector functions complex vector space condition Eq constant complex vectors continuous complex vector continuous function continuous solution cyclic functional equation cyclic permutation D. Z. Djokovié determined by Eq equa equality exists at least expression Eq ﬁnd ﬁrst equation ﬁxed following form following result form Eq formula Eq function f function given function with values functional equation 15.1 given by Eq given by f(U I. B. Risteski i=max introduced the notations Lemma m+n+k matrix nontrivial solution obtain Eq obtained in I. B. paracyclic parameters put Z1 Quadratic Functional Equation satisﬁes the functional second equation solution is given solution of Eq solved substitute Eq theorem holds tion trivial solution U+V+W V)Im variables vector functional equation Xi+p zero Zi+1 Zn+1