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Functional equations involving means of functions on the complex plane
aequationes mathematicae, 1998The author offers the continuous solutions, mapping \(\mathbb{C}\) into itself, of the functional equation \[ (1/N)\sum_{n=0}^{N} f(z+\omega^{n}\zeta)=f(z)+g(z)h(\zeta) \] (\(N\geq 2;\omega\) is a primitive \(N\)-th root of unity) and its integral analog, which generalize several known and important functional equations.
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Growth of Meromorphic Solutions to Some Complex Functional Equations
Computational Methods and Function Theory, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ding, Jie, Wang, Jun, Ye, Zhuan
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Reasoning about equations and functional dependencies on complex objects
IEEE Transactions on Knowledge and Data Engineering, 1994Virtually all semantic or object-oriented data models assume that objects have an identity separate from any of their parts, and allow users to define complex object types in which part values may be any other objects. This often results in a choice of query language in which a user can express navigating from one object to another by following a ...
Martin F. van Bommel, Grant E. Weddell
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Hirzebruch Functional Equations and Krichever Complex Genera
Mathematical Notes, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Bogomolny Field Equations and the Double-Complex Function Method
International Journal of Theoretical Physics, 1999zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Equations. Functions of one variable. Complex numbers
1999Let k be the number of changes of sign in the sequence of coefficients a n , an −1, … , a1, a0 in (2.8). The number of positive real roots of P(x) = 0, counting the multiplicities of the roots, is k or k minus a positive even number. If k = 1, the equation has exactly one positive real root.
Knut Sydsæter, Arne Strøm, Peter Berck
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Differential Equations, Input Functions, Complex Exponentials, and Transfer Functions
2014Differential system equations describe the dynamic relationship between an input driving the system, and one of the power variables within the energetic system. We simplify, or linearize, the individual energetic element equations, in order to derive a system equation which is an ordinary differential equation with constant coefficients, a form which ...
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On a class of complex functional equations
2007The author investigates functional equations of the form \[ C(z,f(p(z)))={A(z,f(z))\over B(z,f(z))}, \] where \(p(z)\) is a complex polynomial and \(A(z,y)\), \(B(z,y)\), \(C(z,y)\) are polynomials of \(y\) with rational coefficients. Under certain assumptions, the main results show that the transcedental meromorphic solutions of the above equation ...
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Proof of equation of complex variable function
International Conference on Applied Statistics, Computational Mathematics, and Software Engineering (ASCMSE 2022), 2022Hanzhi Liu, Zhaohang Wang
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On a functional equation connected with a property of complex numbers
Journal of Interdisciplinary Mathematics, 2003In this paper we determine the general solution of the equation [ f (x) + f (y)][ f (u) + f (v)] = f (xu − yv) + f (xv + yu) for all x, y, u,v ∈ ℝ without assuming any regularity condition on the u...
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