• Aequat. Math. (IF 0.851) Pub Date : 2020-10-20
Tibor Kiss

Let $$I\subseteq \mathbb {R}$$ be a nonempty open subinterval. We say that a two-variable mean $$M:I\times I\rightarrow \mathbb {R}$$ enjoys the balancing property if, for all $$x,y\in I$$, the equality \begin{aligned} {M\big (M(x,M(x,y)),M(M(x,y),y)\big )=M(x,y)} \end{aligned}(1) holds. The above equation has been investigated by several authors. The first remarkable step was made by Georg Aumann

更新日期：2020-10-20
• Aequat. Math. (IF 0.851) Pub Date : 2020-10-06
Rahul Thakur, Ruchi Das

In this paper, we study variants of transitivity and sensitivity via Furstenberg families for iterated function systems (IFSs). Using the concept of skew product transformation of an IFS, we obtain results related to characterizations of the concepts studied. Also results regarding the inverse, conjugacy and product of IFSs are studied. Wherever necessary examples and counterexamples are provided related

更新日期：2020-10-06
• Aequat. Math. (IF 0.851) Pub Date : 2020-09-30
Thomas Vetterlein

An orthogonality space is a set together with a symmetric and irreflexive binary relation. Any linear space equipped with a reflexive and anisotropic inner product provides an example: the set of one-dimensional subspaces together with the usual orthogonality relation is an orthogonality space. We present simple conditions to characterise the orthogonality spaces that arise in this way from finite-dimensional

更新日期：2020-09-30
• Aequat. Math. (IF 0.851) Pub Date : 2020-09-30
László Losonczi, Zsolt Páles, Amr Zakaria

Given two functions $$f,g:I\rightarrow \mathbb {R}$$ and a probability measure $$\mu$$ on the Borel subsets of [0, 1], the two-variable mean $$M_{f,g;\mu }:I^2\rightarrow I$$ is defined by \begin{aligned} M_{f,g;\mu }(x,y) :=\bigg (\frac{f}{g}\bigg )^{-1}\left( \frac{\int _0^1 f\big (tx+(1-t)y\big )d\mu (t)}{\int _0^1 g\big (tx+(1-t)y\big )d\mu (t)}\right) \quad (x,y\in I). \end{aligned} This

更新日期：2020-09-30
• Aequat. Math. (IF 0.851) Pub Date : 2020-09-07
Steve Alpern, Bo Chen, Adam J. Ostaszewski

Consider an odd-sized jury, which determines a majority verdict between two equiprobable states of Nature. If each juror independently receives a binary signal identifying the correct state with identical probability p, then the probability of a correct verdict tends to one as the jury size tends to infinity (Marquis de Condorcet in Essai sur l’application de l’analyse à la probabilité des décisions

更新日期：2020-09-08
• Aequat. Math. (IF 0.851) Pub Date : 2020-09-02
Antal Joós

The maximum separation problem is to find the maximum of the minimum pairwise distance of n points in a planar body $${\mathcal {B}}$$ on the Euclidean plane. In this paper this problem will be considered if $${\mathcal {B}}$$ is the equilateral triangle of side length 1 and the number of points is 13. We will present the exact separation distance of 13 points in the equilateral triangle of side length

更新日期：2020-09-03
• Aequat. Math. (IF 0.851) Pub Date : 2020-09-01
Fei Deng, Zehui Shao, Aleksander Vesel

For a nondecreasing sequence of integers $$S=(s_1, s_2, \ldots )$$ an S-packing k-coloring of a graph G is a mapping from V(G) to $$\{1, 2,\ldots ,k\}$$ such that vertices with color i have pairwise distance greater than $$s_i$$. By setting $$s_i = d + \lfloor \frac{i-1}{n} \rfloor$$ we obtain a (d, n)-packing coloring of a graph G. The smallest integer k for which there exists a (d, n)-packing coloring

更新日期：2020-09-01
• Aequat. Math. (IF 0.851) Pub Date : 2020-08-28
Li Ying

Stembridge introduced the notion of stability for Kronecker triples, which generalizes Murnaghan’s classical stability result for Kronecker coefficients. Sam and Snowden proved a conjecture of Stembridge concerning stable Kronecker triples, and they also showed an analogous result for Littlewood–Richardson coefficients. Heisenberg coefficients are Schur structure constants of the Heisenberg product

更新日期：2020-08-28
• Aequat. Math. (IF 0.851) Pub Date : 2020-08-27
D. E. Ferreyra, F. E. Levis, A. N. Priori, N. Thome

In this paper, we introduce a new generalized inverse, called weak core inverse (or, in short, WC inverse) of a complex square matrix. This new inverse extends the notion of the core inverse defined by Baksalary and Trenkler (Linear Multilinear Algebra 58(6):681–697, 2010). We investigate characterizations, representations, and properties for this generalized inverse. In addition, we introduce weak

更新日期：2020-08-27
• Aequat. Math. (IF 0.851) Pub Date : 2020-08-25
Włodzimierz Fechner, Zsolt Páles

The notions of quasiconvexity, Wright convexity and convexity for functions defined on a metric Abelian group are introduced. Various characterizations of such functions, the structural properties of the functions classes so obtained are established and several well-known results are extended to this new setting.

更新日期：2020-08-26
• Aequat. Math. (IF 0.851) Pub Date : 2020-08-25
M. Ayoubi, D. Zeglami, Y. Aissi

Let M be a topological monoid, let $$\psi :M\rightarrow M$$ be a continuous anti-homomorphism of M, and let $$\mu :M\rightarrow {\mathbb {C}}$$ be a continuous multiplicative function such that $$\mu (x\psi (x))=1$$ for all $$x\in M$$. We describe, in terms of multiplicative functions, additive functions and characters of 2-dimensional representations of M, the solutions (w, g), where $$w,g:M\rightarrow 更新日期：2020-08-25 • Aequat. Math. (IF 0.851) Pub Date : 2020-08-20 Henrik Stetkær We derive an algebraic version over an algebraically closed field k with characteristic \(\ne 2$$ of Yang’s Small Dimension Lemma. With its help we describe the k-valued solutions of d’Alembert’s functional equation on semigroups S in terms of multiplicative functions and irreducible, 2-dimensional representations of S.

更新日期：2020-08-20
• Aequat. Math. (IF 0.851) Pub Date : 2020-08-19
Eliza Jabłońska

Let X be a real Polish vector space, $$D\subset X$$ be a universally Baire non-Haar-meager set, and let $$f:X\rightarrow \mathbb {R}$$ satisfy $$f(x+y)-f(x)-f(y)\in \mathbb {Z}$$ for all $$x,y\in X$$ and $$f(D)\subset (-\frac{1}{3},\frac{1}{3})+\mathbb {Z}$$. We prove that there exists a unique linear functional $$L:X\rightarrow \mathbb {R}$$ with $$f(x)-L(x)\in \mathbb {Z}$$ for $$x\in X$$ and next

更新日期：2020-08-19
• Aequat. Math. (IF 0.851) Pub Date : 2020-08-14
Vishvesh Kumar, Ritumoni Sarma

Let K be a commutative or compact hypergroup. Let $$\mu$$ be a bounded complex-valued Borel measure on K, and let $$T_\mu$$ be the corresponding convolution operator of $$L^1(K)$$. Let S be a bounded linear operator on a Banach space X. We prove that every linear operator $$\Psi : X \rightarrow L^1(K)$$ such that $$\Psi S=T_\mu \Psi$$ is continuous if and only if the pair $$(S,T_\mu )$$ has no critical

更新日期：2020-08-14
• Aequat. Math. (IF 0.851) Pub Date : 2020-07-30
Huhe Han, Denghui Wu

In this paper we show that a spherical convex body C is of constant diameter $$\tau$$ if and only if C is of constant width $$\tau$$, for $$0<\tau <\pi$$. Moreover, some applications to Wulff shapes are given.

更新日期：2020-07-30
• Aequat. Math. (IF 0.851) Pub Date : 2020-07-29
Marek Cezary Zdun

Let I be an interval, X be a metric space and $$\succeq$$ be an order relation on the infinite product $$X^{\infty }$$. Let $$U:X^{\infty }\rightarrow {\mathbb {R}}$$ be a continuous mapping, representing $$\succeq$$, that is such that $$(x_0,x_1,x_2,\ldots )\succeq (y_0,y_1,y_2,\ldots )\Leftrightarrow U(x_0,x_1,x_2,\ldots )\ge U(y_0,y_1,y_2,\ldots )$$. We interpret X as a space of consumption outcomes

更新日期：2020-07-29
• Aequat. Math. (IF 0.851) Pub Date : 2020-07-29
Qian Zhang, Bing Xu, Maoan Han

We consider the invariance of the arithmetic mean with respect to some Cauchy mean-type mapping, namely, we present some results concerning the functional equation \begin{aligned} \left( \frac{f'}{g'}\right) ^{-1}\left( \frac{f(x)-f(y)}{g(x)-g(y)}\right) +\left( \frac{h'}{k'}\right) ^{-1}\left( \frac{h(x)-h(y)}{k(x)-k(y)}\right) =x+y, \quad x\ne y, \ x,y\in I, \end{aligned} where I\subset (0 更新日期：2020-07-29 • Aequat. Math. (IF 0.851) Pub Date : 2020-07-28 Muhammad Nur, Hendra Gunawan We introduce a new 2-norm on a normed space using a semi-inner product g on the space. Using this 2-norm, we propose a formula for the g-angle between 2-dimensional subspaces in the space. Our formula serves as a revision of the one proposed by Nur et al. (Beitr. Algebra Geom. 59(1):133–143, 2018). 更新日期：2020-07-29 • Aequat. Math. (IF 0.851) Pub Date : 2020-07-24 Veerapazham Murugan, Rajendran Palanivel In this paper, we prove that continuous non-PM functions with non-monotonicity height equal to 1 need not be strictly monotone on its range, unlike PM functions. An existence theorem is obtained for the iterative roots of such functions. We also discuss the Hyers–Ulam stability for the functional equation of the iterative root problem. 更新日期：2020-07-24 • Aequat. Math. (IF 0.851) Pub Date : 2020-07-22 Nicole Brillouët-Belluot In this paper we present some methods for solving a large class of composite functional equations. These methods are then applied to the functional equations \begin{aligned} f(a f(x) f(y) + b(f(x)y+f(y)x) +cxy)= & {} f(x) f(y) \end{aligned}(1)\begin{aligned} f(a f(x)^k y + b f(y)^\ell x + cxy)= & {} f(x) f(y) \end{aligned}(2) with \(a, b, c \in {\mathbb {R}} and $$k, \ell \in {\mathbb {N}} 更新日期：2020-07-23 • Aequat. Math. (IF 0.851) Pub Date : 2020-07-13 Gergő Nagy In this paper, we investigate maps on sets of positive operators which are induced by the continuous functional calculus and transform a Kubo–Ando mean \(\sigma$$ into another $$\tau$$. We establish that under quite mild conditions, a mapping $$\phi$$ can have this property only in the trivial case, i.e. when $$\sigma$$ and $$\tau$$ are nontrivial weighted harmonic means and $$\phi$$ stems from

更新日期：2020-07-14
• Aequat. Math. (IF 0.851) Pub Date : 2020-07-13
Gergő Gyula Borus, Attila Gilányi

In the present paper, a general class of linear functional equations is considered and a computer program is described, which determines the exact solutions of systems of equations belonging to this class.

更新日期：2020-07-13
• Aequat. Math. (IF 0.851) Pub Date : 2020-06-30
Mario Krnić, Nicuşor Minculete

We study some interesting characterizations of real inner product spaces expressed in terms of angular distances. We first discuss the equivalence of characterizing an inner product space via the usual angular distance and the p-angular distance. Then, we establish a parametric family of upper bounds for the usual angular distance which also serves as a characterization of an inner product space. As

更新日期：2020-07-01
• Aequat. Math. (IF 0.851) Pub Date : 2020-06-27
Krzysztof Petelczyc, Krzysztof Prażmowski, Mariusz Żynel

The concept of spine geometry over a polar Grassmann space is introduced. We determine conditions under which the structure of lines together with a binary coplanarity relation is a sufficient system of primitive notions for polar spine spaces. These assumptions also allow to characterize polar spine spaces in terms of the binary relation of being in one pencil of lines.

更新日期：2020-06-27
• Aequat. Math. (IF 0.851) Pub Date : 2020-06-25
Douglas R. Anderson, Masakazu Onitsuka

We introduce and study the Hyers–Ulam stability (HUS) of a Cayley quantum (q-difference) equation of first order, where the constant coefficient is allowed to range over the complex numbers. In particular, if this coefficient is non-zero, then the quantum equation has Hyers–Ulam stability for certain values of the Cayley parameter, and we establish the best (minimal) HUS constant in terms of the coefficient

更新日期：2020-06-25
• Aequat. Math. (IF 0.851) Pub Date : 2020-06-23
J. M. Sepulcre, T. Vidal

In this paper we will get a class of functional equations involving a countable set of terms, summed by the well known Bochner–Fejér summation procedure, which are closely associated with the set of almost periodic functions. We will show that the zeros of a prefixed almost periodic function determine analytic solutions of such a functional equation associated with it, and we will obtain other solutions

更新日期：2020-06-24
• Aequat. Math. (IF 0.851) Pub Date : 2020-06-19
Bruce Ebanks

Our main result is the solution of the functional equation $$f(x\sigma (y))+h(\tau (y)x)=2f(x)k(y)$$ for complex-valued functions f, h, k on monoids generated by their squares. Here $$\sigma$$ and $$\tau$$ are involutive automorphisms of the monoid.

更新日期：2020-06-22
• Aequat. Math. (IF 0.851) Pub Date : 2020-06-18
Maxim Korolev, Antanas Laurinčikas

The paper is a continuation of Korolev and Laurinčikas (Aequ Math 93:859–873, 2019), where theorems on the approximation of analytic functions by shifts $$\zeta (s+iht_k)$$, $$h>0$$, $$k\in {\mathbb {N}}$$, and $$t_k$$ are the Gram points, were obtained. In this paper, it is proved, that the set of shifts $$\zeta (s+iht_k)$$ has a positive density in short intervals $$[N, N+M]$$ with $$M=o(N)$$.

更新日期：2020-06-19
• Aequat. Math. (IF 0.851) Pub Date : 2020-06-10
Maciej Sablik

We observe that bisymmetry is in fact the assertion of the Fubini theorem and we describe the form of general bisymmetric operations on some function spaces.

更新日期：2020-06-10
• Aequat. Math. (IF 0.851) Pub Date : 2020-06-03
Dan M. Dăianu, Cristina Mîndruţă

We develop a technique for solving some equations having composite functions as solutions and, on the other hand, a very general procedure for generating new functional equations with predetermined composite solutions.

更新日期：2020-06-03
• Aequat. Math. (IF 0.851) Pub Date : 2020-06-02
Dijana Ilišević, Aleksej Turnšek

In this note we generalize the well-known Wigner’s unitary-antiunitary theorem. For smooth normed spaces X and Y and a surjective mapping $$f :X\rightarrow Y$$ such that $$|[f(x),f(y)]|=|[x,y]|$$, $$x,y\in X$$, where $$[\cdot ,\cdot ]$$ is the unique semi-inner product, we show that f is phase equivalent to either a linear or an anti-linear surjective isometry. When X and Y are smooth real normed spaces

更新日期：2020-06-02
• Aequat. Math. (IF 0.851) Pub Date : 2020-05-30
Luis Barreira, Claudia Valls

We use evolution maps to construct center-stable, center-unstable and center invariant manifolds with optimal regularity for a nonautonomous dynamics with discrete time. The proofs comprise essentially two steps: first we reformulate the original problem in terms of an autonomous problem involving evolutions maps, and then we apply an autonomous result to construct autonomous invariant manifolds that

更新日期：2020-05-30
• Aequat. Math. (IF 0.851) Pub Date : 2020-05-20
G. Hansen, I. Herburt, H. Martini, M. Moszyńska

This is an expository paper about the fundamental mathematical notion of starshapedness, emphasizing the geometric, analytical, combinatorial, and topological properties of starshaped sets and their broad applicability in many mathematical fields. The authors decided to approach the topic in a very broad way since they are not aware of any related survey-like publications dealing with this natural

更新日期：2020-05-20
• Aequat. Math. (IF 0.851) Pub Date : 2020-05-14
Erdal Karapınar, Ali Öztürk, Vladimir Rakočević

In this paper, we investigate sufficient conditions for the existence of solutions to the system \begin{aligned} \left\{ \begin{array}{l} Tx = x,\\ \alpha _i(x) = 0_E,\quad i=1,2,\ldots ,r , \end{array} \right. \end{aligned} where $$0_E$$ is the zero vector of E, and $$\alpha _i :E\rightarrow E \; \; i=1,2,\ldots , r$$ are mappings, T is a mapping satisfying the Pachpatte-contraction.

更新日期：2020-05-14
• Aequat. Math. (IF 0.851) Pub Date : 2020-05-06
Alina Ramona Baias, Dorian Popa

We obtain a result on Ulam stability and on the best Ulam constant for the linear difference equation $$x_{n+3}=ax_{n+2}+bx_{n+1}+c x_n,$$$$a,b,c \in \mathbb {K}$$, where $$\mathbb {K}$$ is one of the fields $$\mathbb {R}$$ or $$\mathbb {C},$$ and $$(x_n)_{n\ge 0}$$ is a sequence in a Banach space X over the field $$\mathbb {K}$$.

更新日期：2020-05-06
• Aequat. Math. (IF 0.851) Pub Date : 2020-05-06
Xianhua Zeng, Xujian Huang

Let $$\Gamma ,\Delta$$ be nonempty index sets, and let H, K be inner product spaces. We prove that for $$p\ge 1$$ any surjective phase-isometry between $$\ell ^p(\Gamma ,H)$$ and $$\ell ^p(\Delta , K)$$ is a plus–minus linear isometry. This can be considered as an extension of Wigner’s theorem for real $$\ell ^p(\Gamma , H)$$-type spaces.

更新日期：2020-05-06
• Aequat. Math. (IF 0.851) Pub Date : 2020-02-22

Let x and y be two unit vectors in a normed plane R 2 . We say that x is Birkhoff orthogonal to y if the line through x in the direction y supports the unit disc. A B-measure (Fankhänel in Beitr Algebra Geom 52(2):335-342, 2011) is an angular measure μ on the unit circle for which μ ( C ) = π / 2 whenever C is a shorter arc of the unit circle connecting two Birkhoff orthogonal points. We present a

更新日期：2020-02-22
• Aequat. Math. (IF 0.851) Pub Date : 2020-02-14

Let p be a real number and let $$\varepsilon >0$$. An operator $$T\in \mathbb {B}(\mathscr {H})$$ is called a $$(p,\varepsilon )$$-approximate n-idempotent if \begin{aligned} \Vert T^nx- Tx\Vert \le \varepsilon \Vert x\Vert ^p\qquad (x\in \mathscr {H})\,. \end{aligned} In this note, we remark that if $$p\ne 1$$, then T is an n-idempotent. If $$p=1$$, the operator T is a self-adjoint contraction

更新日期：2020-02-14
• Aequat. Math. (IF 0.851) Pub Date : 2020-01-27
Karol Baron

In the original publication, Example 2.2 was incorrectly published.

更新日期：2020-01-27
• Aequat. Math. (IF 0.851) Pub Date : 2020-01-23
Zenon Moszner

We solve in some cases the equation in the definition of the concomitant of a geometric object for each of the four functions in this equation. Remarks and examples are given, too.

更新日期：2020-01-23
• Aequat. Math. (IF 0.851) Pub Date : 2020-01-18
Jacek Chudziak

The well known Goldstein–Einhorn probability weighting functions have been characterized by Gonzalez and Wu using the linear in log odds preference condition. We provide an alternative way of deriving this class of functions. It is based on the concept of indifference prices.

更新日期：2020-01-18
• Aequat. Math. (IF 0.851) Pub Date : 2020-01-17
Chaimaa Benzarouala, Lahbib Oubbi

We introduce the general functional equation \begin{aligned} \sum _{i=1}^m A_i( f(\varphi _i (\bar{x}))) + b = 0, \quad \bar{x} := (x_1, x_2, \dots , x_n) \in X^n, \end{aligned} and study its Ulam–Hyers-stability and hyperstability, using a fixed point approach, where m and n are positive integers, f is a mapping from a vector space X into a Banach space $$(Y, \Vert \ \Vert )$$, and, for every

更新日期：2020-01-17
• Aequat. Math. (IF 0.851) Pub Date : 2020-01-14
Monika Nowicka, Alfred Witkowski

We provide optimal bounds for the tangent and hyperbolic sine means in terms of various weighted means of the arithmetic and geometric means.

更新日期：2020-01-14
• Aequat. Math. (IF 0.851) Pub Date : 2020-01-11
Lucio R. Berrone

Several results concerning the homomorphism functional equation \begin{aligned} f\left( x\vee y\right) =f\left( x\right) \vee f\left( y\right) , \end{aligned} in the class of semilattices, as well as other similar equations, are presented in the paper.

更新日期：2020-01-11
• Aequat. Math. (IF 0.851) Pub Date : 2019-11-30
Omar Ajebbar, Elhoucien Elqorachi

Given a semigroup S generated by its squares and equipped with an involutive automorphism $$\sigma$$ and a multiplicative function $$\mu :S\rightarrow \mathbb {C}$$ such that $$\mu (x\sigma (x))=1$$ for all $$x\in S$$, we determine the complex-valued solutions of the following functional equation \begin{aligned} f(xy)-\mu (y)f(\sigma (y)x)=g(x)h(y),\quad x,y\in S. \end{aligned}

更新日期：2019-11-30
• Aequat. Math. (IF 0.851) Pub Date : 2019-11-20
G. García, G. Mora

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.

更新日期：2019-11-20
• Aequat. Math. (IF 0.851) Pub Date : 2019-11-13

Strict monotonicity, lower local uniform monotonicity, upper local uniform monotonicity and their orthogonal counterparts are considered in the case of Musielak–Orlicz function spaces $$L^\Phi (\mu )$$ endowed with the Mazur–Orlicz F-norm as well as in the case of their subspaces $$E^\Phi (\mu )$$ with the F-norm induced from $$L^\Phi (\mu )$$. The presented results generalize some of the results from

更新日期：2019-11-13
• Aequat. Math. (IF 0.851) Pub Date : 2019-11-05
Bruce Ebanks

We solve two Pexiderized extensions of the quadratic functional equation on monoids. The equation is extended by replacing the group inversion in the classical quadratic equation with an involution, which may be either homomorphic or anti-homomorphic. Also two extensions of the Drygas functional equation are solved in the same setting. In all results it is assumed that at least one unknown function

更新日期：2019-11-05
• Aequat. Math. (IF 0.851) Pub Date : 2019-10-22
Miklós Laczkovich

Let G be an Abelian topological semigroup with unit. By a classical result (called Theorem A), if V is a finite dimensional translation invariant linear space of complex valued continuous functions defined on G, then every element of V is an exponential polynomial. More precisely, every element of V is of the form $$\sum _{i=1}^np_i \cdot m_i$$, where $$m_1 ,\ldots ,m_n$$ are exponentials belonging

更新日期：2019-10-22
• Aequat. Math. (IF 0.851) Pub Date : 2019-10-16
Che Tat Ng, Hou Yu Zhao, Xia Lin

In this paper, we determine the complex-valued solutions of the functional equation \begin{aligned} f(x\alpha \sigma (y))+h(\tau (y)x)=2f(x)k(y) \end{aligned} for all $$x,y\in G$$, where G is a group, $$\alpha \in G$$ is a fixed element and $$\sigma ,\tau :G\rightarrow G$$ are involutions.

更新日期：2019-10-16
• Aequat. Math. (IF 0.851) Pub Date : 2019-10-04
Lajos Molnár

In this paper we consider power means of positive Hilbert space operators both in the conventional and in the Kubo–Ando senses. We describe the corresponding isomorphisms (bijective transformations respecting those means as binary operations) on positive definite cones and on positive semidefinite cones in operator algebras. We also investigate the question when those two sorts of power means can be

更新日期：2019-10-04
• Aequat. Math. (IF 0.851) Pub Date : 2019-09-20
Ravindra Kishor Bisht, Nihal Özgür

In this paper, we prove some fixed point theorems under a convex combination of generalized ($$\epsilon -\delta$$) type rational contractions in which the fixed point may or may not be a point of discontinuity. As a by-product we explore some new answers to the open question posed by Rhoades (Contemp Math 72:233–245, 1988). Furthermore, we consider geometric properties of the fixed point set of a

更新日期：2019-09-20
• Aequat. Math. (IF 0.851) Pub Date : 2019-09-19
Gian Luigi Forti, Ekaterina Shulman

The aim of this work is to present and compare the most used methods for proving Hyers–Ulam stability of various classes of functional equations.

更新日期：2019-09-19
• Aequat. Math. (IF 0.851) Pub Date : 2019-09-09
Dorota Głazowska, Justyna Jarczyk, Witold Jarczyk

We determine the form of all semiflows of pairs of weighted quasi-arithmetic means, those over positive dyadic numbers as well as the continuous ones. Then the iterability of such pairs is characterized: necessary and sufficient conditions for a given pair of weighted quasi-arithmetic means to be embeddable into a continuous semiflow are given. In particular, it turns out that surprisingly the existence

更新日期：2019-09-09
• Aequat. Math. (IF 0.851) Pub Date : 2019-09-06
Mihály Bessenyei, Evelin Pénzes

The aim of this note is to present an elementary way to fractals which completely avoids advanced analysis and uses purely naive set theory. The approach relies on fixed point methods, where the role of the Banach contraction principle is replaced by a slightly improved version of the Knaster–Tarski fixed point theorem.

更新日期：2019-09-06
• Aequat. Math. (IF 0.851) Pub Date : 2019-08-24
Eszter Gselmann, Gergely Kiss, Csaba Vincze

The main purpose of this work is to provide the general solutions of a class of linear functional equations. Let $$n\ge 2$$ be an arbitrarily fixed integer, let further X and Y be linear spaces over the field $${\mathbb {K}}$$ and let $$\alpha _{i}, \beta _{i}\in {\mathbb {K}}$$, $$i=1, \ldots , n$$ be arbitrarily fixed constants. We will describe all those functions f, f_{i, j}:X\times Y\rightarrow 更新日期：2019-08-24 • Aequat. Math. (IF 0.851) Pub Date : 2019-08-07 Richárd Grünwald, Zsolt Páles The purpose of this paper is to investigate the equality problem of generalized Bajraktarević means, i.e., to solve the functional equation \begin{aligned} f^{(-1)}\bigg (\frac{p_1(x_1)f(x_1)+\dots +p_n(x_n)f(x_n)}{p_1(x_1)+\dots +p_n(x_n)}\bigg )=g^{(-1)}\bigg (\frac{q_1(x_1)g(x_1)+\dots +q_n(x_n)g(x_n)}{q_1(x_1)+\dots +q_n(x_n)}\bigg ), \end{aligned}(*) which holds for all \((x_1,\dots ,x_n)\in 更新日期：2019-08-07 • Aequat. Math. (IF 0.851) Pub Date : 2019-08-01 Justyna Sikorska We present an approach to solving a number of functional equations for functions with values in abstract convex cones. Such cones seem to be good generalizations of, e.g., families of nonempty compact and convex subsets or nonempty closed, bounded and convex subsets of a normed space. Moreover, we study some related stability problems. 更新日期：2019-08-01 • Aequat. Math. (IF 0.851) Pub Date : 2019-07-29 Janusz Matkowski, Paweł Pasteczka A classical result states that for two continuous, strict means \(M,\,N :I^2 \rightarrow I (I is an interval) there exists a unique (M, N)-invariant mean $$K :I^2 \rightarrow I$$, i.e. such a mean that $$K \circ (M,N)=K$$ and, moreover, the sequence of iterates $$((M,N)^n)_{n=1}^\infty$$ converge to (K, K) pointwise. Recently it was proved that continuity assumption cannot be omitted in general

更新日期：2019-07-29
• Aequat. Math. (IF 0.851) Pub Date : 2019-07-23
Janusz Brzdęk, El-sayed El-hady, Jens Schwaiger

In (Brzdęk and Schwaiger in Aeq Math 92: 975–991, 2018) solutions of far reaching generalizations of the so-called radical functional equation$$f(p(\pi (x)+\pi (y)))=f(x)+f(y)$$ have been investigated. These investigations are continued here by analysing the corresponding stability results, which have been the main subject of several recent papers. We propose a very general and uniform approach.

更新日期：2019-07-23
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