For an abelian group (G,+,0) we consider the functional equation $$f : G \to G, x + f(y + f(x)) = y + f(x + f(y)) \quad (\forall x, y \in G), \quad\quad\qquad (1)$$ most times together with the condition $$f(0) = 0.\qquad\qquad\qquad\qquad\qquad (0)$$ Our main question is whether a solution of $${(1) \wedge (0)}$$ must be additive, i.e., an endomorphism of G. We shall answer this question in the negative (Example 3.14) Rätz (Aequationes Math 81:300, 2011
In this paper we give a reverse generalization of the generalized H�older and Minkowski type inequal...
For any finite group $G$, any finite $G$-set $X$ and any field $F$, we consider the vector space $F^...
In this paper, we obtain sharp bounds for the norm of pre-Schwarzian derivatives of certain analytic...
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Inspired by a problem by J. Matkowski in [Aequationes Math. 80 (2010), no. 1-2, 181–192; MR2736949] ...
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The main purpose of this work is to provide the general solutions of a class of linear functional eq...
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In this paper we give a reverse generalization of the generalized H�older and Minkowski type inequal...
For any finite group $G$, any finite $G$-set $X$ and any field $F$, we consider the vector space $F^...
In this paper, we obtain sharp bounds for the norm of pre-Schwarzian derivatives of certain analytic...
AbstractLet (G,+) be an abelian group and let E be a normed space. A mapping f:G→E is called ε-quadr...
AbstractWe investigate some inequalities connected with the Hyers–Ulam stability of three functional...
AbstractIn this paper, we obtain the general solution and stability of the Cauchy–Jensen functional ...
In the present paper, we determine the solutions f : S!H of the generalized quadratic functional equ...
Inspired by a problem by J. Matkowski in [Aequationes Math. 80 (2010), no. 1-2, 181–192; MR2736949] ...
AbstractWe study two criterions of cyclicity for divisor class groups of function fields, the first ...
AbstractLet G be a finite abelian group of order n. For a complex valued function f on G let f̂ deno...
The main purpose of this work is to provide the general solutions of a class of linear functional eq...
AbstractLet X be a real linear space. We characterize continuous on rays solutions f,g:X→R of the eq...
AbstractWe prove the stability of a generalization of the Bourgin's result on approximate ring homom...
AbstractThe aim of this paper is to study the stability problem of the d'Alembert type and Jensen ty...
AbstractIn this paper we obtain the general solution of the quadratic Jensen type functional equatio...
In this paper we give a reverse generalization of the generalized H�older and Minkowski type inequal...
For any finite group $G$, any finite $G$-set $X$ and any field $F$, we consider the vector space $F^...
In this paper, we obtain sharp bounds for the norm of pre-Schwarzian derivatives of certain analytic...