Alienation of two general linear functional equations

Szostok, Tomasz

doi:10.1007/s00010-019-00667-4

Cited by 11 publications

(4 citation statements)

References 12 publications

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“…It may even happen that for monomial functions of some order some equations are alien and for other orders the same equations are not alien. This effect is similar to the approach presented in [34] by the fourth author. Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.…”

Section: Examplesupporting

confidence: 87%

On a new class of functional equations satisfied by polynomial functions

et al. 2021

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The classical result of L. Székelyhidi states that (under some assumptions) every solution of a general linear equation must be a polynomial function. It is known that Székelyhidi’s result may be generalized to equations where some occurrences of the unknown functions are multiplied by a linear combination of the variables. In this paper we study the equations where two such combinations appear. The simplest nontrivial example of such a case is given by the equation $$\begin{aligned} F(x + y) - F(x) - F(y) = yf(x) + xf(y) \end{aligned}$$ F ( x + y ) - F ( x ) - F ( y ) = y f ( x ) + x f ( y ) considered by Fechner and Gselmann (Publ Math Debrecen 80(1–2):143–154, 2012). In the present paper we prove several results concerning the systematic approach to the generalizations of this equation.

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Section: Examplesupporting

confidence: 87%

On a new class of functional equations satisfied by polynomial functions

et al. 2021

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“…Problems connected to class (1), its generalizations and its applications have been studied by several authors during the last more than 100 years. (Recent related results can be found, among others, in [13,[15][16][17]24]. )…”

Section: Introductionmentioning

confidence: 71%

On linear functional equations modulo $${\mathbb {Z}}$$

Gilányi

Lewicka

2021

Aequat. Math.

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In this paper, we consider the condition $$\sum _{i=0}^{n+1}\varphi _i(r_ix+q_iy)\in {\mathbb {Z}}$$ ∑ i = 0 n + 1 φ i ( r i x + q i y ) ∈ Z for real valued functions defined on a linear space V. We derive necessary and sufficient conditions for functions satisfying this condition to be decent in the following sense: there exist functions $$f_i:V\rightarrow {\mathbb {R}}$$ f i : V → R , $$g_i:V\rightarrow {\mathbb {Z}}$$ g i : V → Z such that $$\varphi _i=f_i+g_i$$ φ i = f i + g i , $$(i=0,\dots ,n+1)$$ ( i = 0 , ⋯ , n + 1 ) and $$\sum _{i=0}^{n+1}f_i(r_ix+q_iy)=0$$ ∑ i = 0 n + 1 f i ( r i x + q i y ) = 0 for all $$x, y\in V$$ x , y ∈ V .

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“…The concepts of the alienness and the strong alienness of functional equations were introduced by Jean Dhombres in his paper [3]. These properties were studied by several authors during the last more than 30 years (cf., e.g., [4] and [9]).…”

Section: Attila Gilányi: Computer Aided Investigation Of Alienness Of...mentioning

confidence: 99%

Report of Meeting: The Twenty-second Debrecen–Katowice Winter Seminar on Functional Equations and Inequalities Hajdúszoboszló (Hungary), February 1–4, 2023

2023

Annales Mathematicae Silesianae

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The 27 participants came from the University of Silesia (Poland), the University of Debrecen (Hungary), the University of Rzeszów (Poland) and the Kazimierz Wielki University (Poland), 8 from the first, 16 from the second, 2 from the third and 1 from the fourth university.Professor Zsolt Páles opened the Seminar and welcomed the participants to Hajdúszoboszló.The scientific talks presented at the Seminar focused on the following topics: equations in a single variable and in several variables, iterative equations, equations on algebraic structures, functional inequalities, Hyers-Ulam stability, functional equations and inequalities involving mean values, generalized convexity and Walsh-Fourier analysis. Interesting discussions were generated by the talks.

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Alienation of two general linear functional equations

Cited by 11 publications

References 12 publications

On a new class of functional equations satisfied by polynomial functions

On a new class of functional equations satisfied by polynomial functions

On linear functional equations modulo $${\mathbb {Z}}$$

Report of Meeting: The Twenty-second Debrecen–Katowice Winter Seminar on Functional Equations and Inequalities Hajdúszoboszló (Hungary), February 1–4, 2023

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