A composite functional equation on groups
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DOI: 10.1007/s00010-016-0454-7
Abstract: We analyse the composite functional equation $$f(x+2f(y))=f(x)+y+f(y)$$f(x+2f(y))=f(x)+y+f(y) on certain groups. In particular we give a description of solutions on abelian 3-groups and finitely generated free abelian groups. This is motivated by a work of Pál… read more here.
Keywords: equation groups; functional equation; abelian groups; equation ... See more keywords
On the generalized Fréchet functional equation with constant coefficients and its stability
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DOI: 10.1007/s00010-017-0536-1
Abstract: We study a generalization of the Fréchet functional equation, stemming from a characterization of inner product spaces. We show, in particular, that under some weak additional assumptions each solution of such an equation is additive.… read more here.
Keywords: equation constant; generalized chet; functional equation; equation ... See more keywords
Generalized convolutions and the Levi-Civita functional equation
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DOI: 10.1007/s00010-018-0578-z
Abstract: In Borowiecka et al. (Bernoulli 21(4):2513–2551, 2015) the authors show that every generalized convolution can be used to define a Markov process, which can be treated as a Lévy process in the sense of this convolution.… read more here.
Keywords: civita functional; convolutions levi; functional equation; generalized convolutions ... See more keywords
More about Wilson’s functional equation
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DOI: 10.1007/s00010-019-00654-9
Abstract: Let G be a group with an involution $$x \mapsto x^*$$ x ↦ x ∗ , let $$\mu :G \rightarrow \mathbb {C}$$ μ : G → C be a multiplicative function such that $$\mu (xx^*)… read more here.
Keywords: functional equation; wilson functional;
On the Ulam–Hyers stability of the complex functional equation $$\varvec{F(z)+F(2z)+\cdots +F(nz)=0}$$
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DOI: 10.1007/s00010-019-00693-2
Abstract: In the present paper we prove that the complex functional equation $$F(z)+F(2z)+\cdots +F(nz)=0$$, $$n\ge 2$$, $$z\in {\mathbb {C}}{\setminus }( -\infty ,0] $$, is stable in the generalized Hyers–Ulam sense. read more here.
Keywords: hyers stability; stability complex; functional equation; complex functional ... See more keywords
On the functional equation $${\varvec{f}}({\varvec{x}})+{\varvec{f}}({\varvec{y}})=\mathbf{max} \{{\varvec{f}}({\varvec{xy}}),{\varvec{f}}({\varvec{xy}}^{-{\varvec{1}}})\}$$f(x)+f(y)=max{f(xy),f(xy-1)} on groups
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DOI: 10.1007/s00013-017-1061-0
Abstract: We analyse the functional equation $$\begin{aligned} f(x)+f(y)=\max \{f(xy),f(xy^{-1})\} \end{aligned}$$f(x)+f(y)=max{f(xy),f(xy-1)}for a function $$f:G\rightarrow \mathbb R$$f:G→R where G is a group. Without further assumption it characterises the absolute value of additive functions. In addition $$\{z\in G\mid f(z)=0\}$${z∈G∣f(z)=0}… read more here.
Keywords: varvec varvec; varvec; functional equation; max ... See more keywords
D’Alembert’s Matrix Functional Equation with an Endomorphism on Abelian Groups
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DOI: 10.1007/s00025-020-01265-6
Abstract: Let G be an abelian group, let $$M_{2}(\mathbb {C})$$ be the algebra of complex $$2\times 2$$ matrices, and let $$\varphi :G\rightarrow G$$ be an endomorphism that need not be involutive. We determine the solutions $$\Phi… read more here.
Keywords: endomorphism; functional equation; rightarrow mathbb; phi ... See more keywords
Alienation of the Quadratic And Additive Functional Equations
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DOI: 10.1007/s10476-019-0869-1
Abstract: Let G, H be uniquely 2-divisible Abelian groups. We study the solutions f, g: G → H of Pexider type functional equation (*)$$f(x+y)+f(x-y)+g(x+y)=2f(x)+2f(y)+g(x)+g(y),$$f(x+y)+f(x−y)+g(x+y)=2f(x)+2f(y)+g(x)+g(y), resulting from summing up the well known quadratic functional equation and additive… read more here.
Keywords: quadratic additive; alienation quadratic; additive functional; equation ... See more keywords
Hankel transform, Langlands functoriality and functional equation of automorphic L-functions
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DOI: 10.1007/s11537-019-1650-8
Abstract: This is a survey on recent works of Langlands’s work on functoriality conjectures and related works including the works of Braverman and Kazhdan on the functional equation of automorphic L -functions. Efforts have been made… read more here.
Keywords: automorphic functions; transform langlands; functional equation; hankel transform ... See more keywords
On Approximately of a $$\sigma -$$σ-Quadratic Functional Equation on a Set of Measure Zero
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DOI: 10.1007/s11785-016-0594-8
Abstract: Let $${\mathbb {C}}$$C be the set of complex numbers, X be a normed space and Y be a Banach space. We investigate the Hyers-Ulam stability theorem when $$f:{\mathbb {C}}\rightarrow Y$$f:C→Y satisfy the following $$\sigma -$$σ-quadratic… read more here.
Keywords: sigma quadratic; measure; functional equation; approximately sigma ... See more keywords
Entire and Meromorphic Solutions of the Functional Equation $$f^n+g^n+h^n=1$$fn+gn+hn=1 and Differential Equations
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DOI: 10.1007/s40315-018-0258-y
Abstract: In this paper, we study Fermat-type functional equations $$f^n+g^n+h^n=1$$fn+gn+hn=1 in the complex plane. Alternative proofs of the known results for entire and meromorphic solutions of such equations are given. Moreover, some conditions on degrees of… read more here.
Keywords: equation differential; differential equations; entire meromorphic; solutions functional ... See more keywords