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ON A COMPOSITE FUNCTIONAL EQUATION
Demonstratio Mathematica, 2003 The composite functional equation \[ f(xG(f(x))) = f(x)G(f(x)), \quad x \in \mathbb R_+,\tag{1} \] is considered. \textit{P. Kahlig}, \textit{A. Matkowska} and \textit{J. Matkowski} [Aequationes Math. 52, 260--283 (1996; Zbl 0861.39013)] dealt with the special case: \(G(u) = u^p\). Here the continuous solutions \(f: \mathbb R_+ \to \mathbb R_+\) of (1)
Matkowski, Janusz, Okrzesik, Jolanta
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The Laplace transform of Dirichlet L-functions
Nonlinear Analysis, 2012 In the paper, a formula for the Laplace transform of the square of Dirichlet L-functions on the critical line is obtained.
Aidas Balčiūnas, Antanas Laurinčikas
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On a functional equation of Bellman
Journal of Mathematical Analysis and Applications, 1978 where x > 0, fr
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On Jensen's functional equation
Aequationes Mathematicae, 1992 The following is offered as main result. Let \((G,\cdot)\) and \((H,+)\) be abelian groups, and \(e\) the neutral element of \((G,\cdot)\). The solutions \(f: G\to H\) of \(f(xy)+f(xy^{-1})=2f(x)\), \(f(e)=0\) are exactly the homomorphisms of \(G\to H\) if, and only if, either \(H\) has no element of order 2 or \([G:G^ 2]\leq 2\), where \(G^ 2:=\{x^ 2 ...
Vasudeva, H.L., Parnami, J.C.
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On a “square” functional equation [PDF]
Pacific Journal of Mathematics, 1974 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Some Suzuki-type fixed point theorems for generalized multivalued mappings and applications
Fixed Point Theory and Applications, 2011 In this article we obtain a Suzuki-type generalization of a fixed point theorem for generalized multivalued mappings of Ćirić (Matematićki Vesnik, 9(24), 265-272, 1972).
Đorić Dragan +1 more
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Stability of generalized Newton difference equations
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2012 In the paper we discuss a stability in the sense of the generalized Hyers-Ulam-Rassias for functional equations Δn(p, c)φ(x) = h(x), which is called generalized Newton difference equations, and give a sufficient condition of the generalized Hyers-Ulam ...
Wang Zhihua, Shi Yong-Guo
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On the Neumann problem for a hyperbolic partial differential equation of second order [PDF]
Rendiconti di Matematica e delle Sue Applicazioni, 1998 The paper concerns the Neumann problem for the equation uxy = c. By using the method of G. Fichera, introduced in paper [5] devoted to the Dirichlet problem, necessary and sufficient conditions for the existence of the solutions are found.
A. Borzymowski, M. Shaieb
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Journal of Mathematical Analysis and Applications, 2005 In analogy to the ``quadratic functional equation'' \[ f(x+y)+f(x-y)=2f(x)+2f(y), \] that is, \(_s\Delta^2_y f(x)=2f(y),\) the authors call \[ f(2x+y)-4f(x+y)+6f(y)-4f(x-y)+f(2x-y)=4! f(x) \] (rather than \(_s\Delta^4_y f(x):= f(x+2y)-4f(x+y)+6f(x)-4f(x-y)+f(x-2y)=4! f(y)\)) ``quartic functional equation''. They offer its general solution from the real
Sung Mo Im, In Sung Hwang, Sang Han Lee
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On the superstability of the cosine and sine type functional equations
Annales Universitatis Paedagogicae Cracoviensis: Studia Mathematica, 2016 In this paper, We study the superstablity problem of the cosine and sine type functional equations: f(xσ(y)a)+f(xya)=2f(x)f(y) and f(xσ(y)a)-f(xya)=2f(x)f(y), where f:S → C is a complex valued function; S is a semigroup; σ is an involution of
Fouad Lehlou +3 more
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