Acta Mathematica Hungarica, ISSN 0236-5294, 4/2018, Volume 154, Issue 2, pp. 530 - 544

The purpose of this paper is to show that functions that derivate the two-variable product function and one of the exponential, trigonometric or hyperbolic...

39B40 | 39B22 | algebraic derivation | derivation for trigonometric functions | Mathematics, general | Mathematics | derivation for hyperbolic functions | 39B50 | MATHEMATICS | APPROXIMATE DERIVATIONS | LINEAR FUNCTIONS | EQUATION | Mathematics - Classical Analysis and ODEs

39B40 | 39B22 | algebraic derivation | derivation for trigonometric functions | Mathematics, general | Mathematics | derivation for hyperbolic functions | 39B50 | MATHEMATICS | APPROXIMATE DERIVATIONS | LINEAR FUNCTIONS | EQUATION | Mathematics - Classical Analysis and ODEs

Journal Article

Acta Mathematica Hungarica, ISSN 0236-5294, 12/2017, Volume 153, Issue 2, pp. 350 - 355

Let $${(X, \mathscr{L}, \lambda)}$$ ( X , L , λ ) and $${(Y, \mathscr{M}, \mu)}$$ ( Y , M , μ ) be finite measure spaces for which there exist $${A \in...

39B52 | 91B99 | primary 26E60 | functional equation | 39B22 | generalized (quasi-arithmetic) mean | commuting mapping | secondary 28E99 | 60B99 | Mathematics, general | Mathematics | MATHEMATICS | PREFERENCES | Computer science | Mathematics - Classical Analysis and ODEs

39B52 | 91B99 | primary 26E60 | functional equation | 39B22 | generalized (quasi-arithmetic) mean | commuting mapping | secondary 28E99 | 60B99 | Mathematics, general | Mathematics | MATHEMATICS | PREFERENCES | Computer science | Mathematics - Classical Analysis and ODEs

Journal Article

Integral Equations and Operator Theory, ISSN 0378-620X, 2015, Volume 81, Issue 4, pp. 455 - 482

Journal Article

Results in Mathematics, ISSN 1422-6383, 12/2019, Volume 74, Issue 4, pp. 1 - 9

The focus of this paper is the equality problem of quasi-arithmetic expressions. This class is a far generalization of the well-known class of quasi-arithmetic...

39B12 | 39B22 | 39B55 | extension theorems | quasi-arithmetic means | Mathematics, general | Mathematics | Quasi-arithmetic expressions | regularity | 39B82 | MATHEMATICS | MATHEMATICS, APPLIED | Equality

39B12 | 39B22 | 39B55 | extension theorems | quasi-arithmetic means | Mathematics, general | Mathematics | Quasi-arithmetic expressions | regularity | 39B82 | MATHEMATICS | MATHEMATICS, APPLIED | Equality

Journal Article

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Full Text
Quadratic functions fulfilling an additional condition along hyperbolas or the unit circle

Aequationes mathematicae, ISSN 0001-9054, 4/2019, Volume 93, Issue 2, pp. 451 - 465

Let $$ S_1 $$ S 1 denote the set of all pairs (x, y) of real numbers that fulfill the condition $$ x^2 - y^2 = 1 $$ x 2 - y 2 = 1 , and $$ S_2 $$ S 2 denote...

Biadditive function | Primary 39B22 | Secondary 39B55 | Analysis | Conditional equation | Mathematics | Combinatorics | Quadratic function | MATHEMATICS | MATHEMATICS, APPLIED | Real numbers | Quadratic equations | Hyperbolas

Biadditive function | Primary 39B22 | Secondary 39B55 | Analysis | Conditional equation | Mathematics | Combinatorics | Quadratic function | MATHEMATICS | MATHEMATICS, APPLIED | Real numbers | Quadratic equations | Hyperbolas

Journal Article

Journal of Global Optimization, ISSN 0925-5001, 5/2014, Volume 59, Issue 1, pp. 165 - 171

In this paper we obtain a result on Hyers–Ulam stability of the linear functional equation in a single variable $$f(\varphi (x)) = g(x) \cdot f(x)$$ f ( φ ( x...

33B15 | Stability | Complete metric group | Functional equation | 11B34 | Banach spaces | Optimization | Economics / Management Science | Euler–Mascheroni constant | 41A30 | 39B22 | Operations Research/Decision Theory | Inequalities | Computer Science, general | Operator mapping | Real Functions | Euler-Mascheroni constant | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | HIGHER-ORDER | Studies | Mathematics | Linear equations | Texts | Mathematical analysis

33B15 | Stability | Complete metric group | Functional equation | 11B34 | Banach spaces | Optimization | Economics / Management Science | Euler–Mascheroni constant | 41A30 | 39B22 | Operations Research/Decision Theory | Inequalities | Computer Science, general | Operator mapping | Real Functions | Euler-Mascheroni constant | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | HIGHER-ORDER | Studies | Mathematics | Linear equations | Texts | Mathematical analysis

Journal Article

Aequationes mathematicae, ISSN 0001-9054, 4/2016, Volume 90, Issue 2, pp. 427 - 448

The theory of regular variation, in its Karamata and Bojanić–Karamata/de Haan forms, is long established and makes essential use of the Cauchy functional...

Gołąb–Schinzel equation | 33B99 | Beurling regular variation | Mathematics | Cauchy equation | 34D05 | 39A20 | self-neglecting functions | circle group | Popa group | 39B22 | Analysis | Beurling’s equation | 26A03 | Combinatorics | Golab-Schinzel equation | MATHEMATICS | REGULAR VARIATION | MATHEMATICS, APPLIED | Beurling's equation | THEOREM | GENERALIZED PEXIDER EQUATION | Functional equations | Homomorphisms | Mathematical analysis | Algebra

Gołąb–Schinzel equation | 33B99 | Beurling regular variation | Mathematics | Cauchy equation | 34D05 | 39A20 | self-neglecting functions | circle group | Popa group | 39B22 | Analysis | Beurling’s equation | 26A03 | Combinatorics | Golab-Schinzel equation | MATHEMATICS | REGULAR VARIATION | MATHEMATICS, APPLIED | Beurling's equation | THEOREM | GENERALIZED PEXIDER EQUATION | Functional equations | Homomorphisms | Mathematical analysis | Algebra

Journal Article

Aequationes mathematicae, ISSN 0001-9054, 2/2019, Volume 93, Issue 1, pp. 21 - 35

We determine continuous bijections f, acting on a real interval into itself, whose k-fold iterate is the quasi-arithmetic mean of all its subsequent iterates...

Polynomial-like iterative equation | Primary 39B22 | 39B12 | Analysis | Iterate | Mathematics | Continuous solution | Combinatorics | Secondary 26A18 | MATHEMATICS | ORDER | MATHEMATICS, APPLIED | BIJECTION

Polynomial-like iterative equation | Primary 39B22 | 39B12 | Analysis | Iterate | Mathematics | Continuous solution | Combinatorics | Secondary 26A18 | MATHEMATICS | ORDER | MATHEMATICS, APPLIED | BIJECTION

Journal Article

Proceedings - Mathematical Sciences, ISSN 0253-4142, 2/2019, Volume 129, Issue 1, pp. 1 - 12

A general solution of the pexiderized functional equation $$\begin{aligned} f(ux+vy,uy-vx, zw)=g(x,y,z)\;h(u,v,w) \end{aligned}$$...

functional equation | Permanent | 39B22 | Mathematics, general | Mathematics | exponential function | 15A15 | multiplicative function | MATHEMATICS

functional equation | Permanent | 39B22 | Mathematics, general | Mathematics | exponential function | 15A15 | multiplicative function | MATHEMATICS

Journal Article

Aequationes mathematicae, ISSN 0001-9054, 12/2019, Volume 93, Issue 6, pp. 1139 - 1157

The equation $$x+g(y+f(x))=y+g(x+f(y))$$ x + g ( y + f ( x ) ) = y + g ( x + f ( y ) ) was introduced by Marcin E. Kuczma in connection with his research on...

Mathematics | Combinatorics | 39B22 | Analysis

Mathematics | Combinatorics | 39B22 | Analysis

Journal Article

Results in Mathematics, ISSN 1422-6383, 2/2014, Volume 65, Issue 1, pp. 251 - 261

We consider singular solutions of the functional equation $${f(xf(x)) = \varphi (f(x))}$$ f ( x f ( x ) ) = φ ( f ( x ) ) where $${\varphi}$$ φ is a given and...

dynamical systems | invariant curves | Dhombres functional equation | periodic orbits | Primary 39B12 | 39B22 | Mathematics, general | Mathematics | iterative functional equation | 37E05 | Secondary 26A18 | Chaotic behavior | Mathematics Subject Classification : Primary 39B12, 39B22, 37E05, Secondary 26A18 | MATHEMATICS | MATHEMATICS, APPLIED

dynamical systems | invariant curves | Dhombres functional equation | periodic orbits | Primary 39B12 | 39B22 | Mathematics, general | Mathematics | iterative functional equation | 37E05 | Secondary 26A18 | Chaotic behavior | Mathematics Subject Classification : Primary 39B12, 39B22, 37E05, Secondary 26A18 | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

Aequationes mathematicae, ISSN 0001-9054, 2/2019, Volume 93, Issue 1, pp. 137 - 148

Two years ago, during the 21st European Conference on Iteration Theory, Gregory Derfel asked: “Does there exist a non-trivial bounded continuous solution of...

Quasi-arithmetic mean | Secondary 39B05 | Functional equations | Primary 39B22 | Analysis | Mathematics | Archetypal equation | Combinatorics | Equations with rescaling | MATHEMATICS | MATHEMATICS, APPLIED | Mathematical analysis

Quasi-arithmetic mean | Secondary 39B05 | Functional equations | Primary 39B22 | Analysis | Mathematics | Archetypal equation | Combinatorics | Equations with rescaling | MATHEMATICS | MATHEMATICS, APPLIED | Mathematical analysis

Journal Article

Aequationes mathematicae, ISSN 0001-9054, 2/2019, Volume 93, Issue 1, pp. 109 - 120

Using a simple dynamical system generated by means M and N which are considered on adjacent intervals, we show how to find their joints, that is means...

Mean | Joiner | Secondary 39B22 | Functional equation of semiconjugacy | Primary 26E60 | Extension of means | Mathematics | Iteration | Attractor | Analysis | Marginal joint of means | Combinatorics | 26A18 | MATHEMATICS | MATHEMATICS, APPLIED | Joining

Mean | Joiner | Secondary 39B22 | Functional equation of semiconjugacy | Primary 26E60 | Extension of means | Mathematics | Iteration | Attractor | Analysis | Marginal joint of means | Combinatorics | 26A18 | MATHEMATICS | MATHEMATICS, APPLIED | Joining

Journal Article

Aequationes mathematicae, ISSN 0001-9054, 2/2019, Volume 93, Issue 1, pp. 239 - 246

Given a set $$T\subset (0, +\infty )$$ T ⊂ ( 0 , + ∞ ) , a function $$c:T\rightarrow \mathbb R$$ c : T → R and a real number p we study continuous solutions...

Simultaneous equations | Secondary 39B12 | Difference equations | Primary 39A13 | 39B22 | Analysis | Equations on restricted domains | Form of continuous solutions | Mathematics | Combinatorics | 39B72 | MATHEMATICS | MATHEMATICS, APPLIED | Mathematical analysis

Simultaneous equations | Secondary 39B12 | Difference equations | Primary 39A13 | 39B22 | Analysis | Equations on restricted domains | Form of continuous solutions | Mathematics | Combinatorics | 39B72 | MATHEMATICS | MATHEMATICS, APPLIED | Mathematical analysis

Journal Article

Aequationes mathematicae, ISSN 0001-9054, 10/2018, Volume 92, Issue 5, pp. 935 - 947

The aim of this paper is to describe the solution (f, g) of the equation $$\begin{aligned}{}[f(x)-f(y)]g'(\alpha x+(1-\alpha )y)= [g(x)-g(y)]f'(\alpha...

Mean value theorem | 39B22 | Analysis | Functional equation | Mathematics | Linearly dependent functions | Combinatorics | MATHEMATICS | MATHEMATICS, APPLIED | QUADRATIC POLYNOMIALS | PROPERTY | Differential calculus | Cauchy problems | Functional equations

Mean value theorem | 39B22 | Analysis | Functional equation | Mathematics | Linearly dependent functions | Combinatorics | MATHEMATICS | MATHEMATICS, APPLIED | QUADRATIC POLYNOMIALS | PROPERTY | Differential calculus | Cauchy problems | Functional equations

Journal Article

Aequationes mathematicae, ISSN 0001-9054, 12/2016, Volume 90, Issue 6, pp. 1071 - 1085

We consider regularity for solutions of a class of de Rham’s functional equations. Under some smoothness conditions of functions making up the equation, we...

39B52 | 26A30 | Singularity | 39B22 | Analysis | 26A27 | De Rham’s functional equations | Mathematics | Combinatorics | Functional equations | Mathematical analysis | Smoothness | Regularity | Linear functions

39B52 | 26A30 | Singularity | 39B22 | Analysis | 26A27 | De Rham’s functional equations | Mathematics | Combinatorics | Functional equations | Mathematical analysis | Smoothness | Regularity | Linear functions

Journal Article

Aequationes mathematicae, ISSN 0001-9054, 12/2015, Volume 89, Issue 6, pp. 1415 - 1431

Joining previous authors, we propose axiomatic properties that yield the mean as the unique measure of center of a data set. In addition to familiar properties...

translativity | functional equations | median | 39B22 | Analysis | Decomposability | Secondary 26E60 | Mathematics | Combinatorics | Primary 60A05

translativity | functional equations | median | 39B22 | Analysis | Decomposability | Secondary 26E60 | Mathematics | Combinatorics | Primary 60A05

Journal Article

Aequationes mathematicae, ISSN 0001-9054, 4/2019, Volume 93, Issue 2, pp. 445 - 449

In this short note we show that a weak version of Bernstein’s characterization of the normal distribution implies the local integrability of a measurable...

Measurability | Characteristic function | Cauchy functional equation | 39B22 | 60E10 | Normal distribution | Analysis | Local integrability | 62E10 | Bernstein’s characterization theorem | Mathematics | Combinatorics | MATHEMATICS | MATHEMATICS, APPLIED | Bernstein's characterization theorem | Theorems | Statistical analysis | Functional equations | Linearity

Measurability | Characteristic function | Cauchy functional equation | 39B22 | 60E10 | Normal distribution | Analysis | Local integrability | 62E10 | Bernstein’s characterization theorem | Mathematics | Combinatorics | MATHEMATICS | MATHEMATICS, APPLIED | Bernstein's characterization theorem | Theorems | Statistical analysis | Functional equations | Linearity

Journal Article

Aequationes mathematicae, ISSN 0001-9054, 8/2016, Volume 90, Issue 4, pp. 809 - 815

In this paper, we present an extention of Hyers–Ulam stability of Sahoo–Riedel’s points for real-valued differentiable functions on [a, b] and then we obtain...

39B22 | 26A24 | Analysis | Sahoo–Riedel equations | Mathematics | Combinatorics | Sahoo–Riedel’s points | Hyers–Ulam stability | Flett’s points | 39B82 | Stability

39B22 | 26A24 | Analysis | Sahoo–Riedel equations | Mathematics | Combinatorics | Sahoo–Riedel’s points | Hyers–Ulam stability | Flett’s points | 39B82 | Stability

Journal Article

Aequationes mathematicae, ISSN 0001-9054, 10/2015, Volume 89, Issue 5, pp. 1293 - 1310

The Cauchy functional equation is not only the most important single functional equation, it is also central to regular variation. Classical Karamata regular...

39A20 | 33B99 | 39B22 | Gołąb–Schinzel functional equation | Analysis | Beurling regular variation | Mathematics | 26A03 | Regular variation | Combinatorics | Beurling’sequation | 34D05

39A20 | 33B99 | 39B22 | Gołąb–Schinzel functional equation | Analysis | Beurling regular variation | Mathematics | 26A03 | Regular variation | Combinatorics | Beurling’sequation | 34D05

Journal Article

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