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  • On graphs with equal total domination and Grundy total domination numbers
    Aequat. Math. (IF 0.851) Pub Date : 2021-01-21
    Tanja Dravec, Marko Jakovac, Tim Kos, Tilen Marc

    A sequence \((v_1,\ldots ,v_k)\) of vertices in a graph G without isolated vertices is called a total dominating sequence if every vertex \(v_i\) in the sequence totally dominates at least one vertex that was not totally dominated by \(\{v_1,\ldots , v_{i-1}\}\) and \(\{v_1,\ldots ,v_k\}\) is a total dominating set of G. The length of a shortest such sequence is the total domination number of G (\(\gamma

    更新日期:2021-01-21
  • On the Hyers–Ulam stability of certain nonautonomous and nonlinear difference equations
    Aequat. Math. (IF 0.851) Pub Date : 2021-01-15
    Davor Dragičević

    This article is devoted to the study of certain nonautonomous and nonlinear difference equations of higher order. Our main objective is to formulate sufficient conditions under which the class of difference equations we consider exhibits Hyers–Ulam stability. Our methods rely on the relationship between Hyers–Ulam stability and hyperbolicity for nonautonomous systems.

    更新日期:2021-01-15
  • Completely monotonic ratios of basic and ordinary gamma functions
    Aequat. Math. (IF 0.851) Pub Date : 2021-01-02
    Christian Berg, Asena Çetinkaya, Dmitrii Karp

    We investigate conditions for logarithmic complete monotonicity of product ratios of gamma and q-gamma functions whose arguments are linear functions of the variable. We give necessary and sufficient conditions in terms of nonnegativity of a certain explicitly written measure in the q case and of a certain elementary function in the classical \(q=1\) case. In the latter case we further provide simple

    更新日期:2021-01-02
  • The conditional distributivity condition for T-uninorms revisited
    Aequat. Math. (IF 0.851) Pub Date : 2021-01-02
    Wenwen Zong, Yong Su

    This paper studies the conditional distributivity for T-uninorms over uninorms in the most general setting, transforming it into the (conditional) distributivity equation involving two uninorms.

    更新日期:2021-01-02
  • Quasi-arithmetic-type invariant means on probability space
    Aequat. Math. (IF 0.851) Pub Date : 2021-01-01
    Beata Deręgowska, Paweł Pasteczka

    For a family \((\mathscr {A}_x)_{x \in (0,1)}\) of integral quasi-arithmetic means satisfying certain measurability-type assumptions we search for an integral mean K such that \(K\big ((\mathscr {A}_x(\mathbb {P}))_{x \in (0,1)}\big )=K(\mathbb {P})\) for every compactly supported probability Borel measure \(\mathbb {P}\). Also some results concerning the uniqueness of invariant means will be given

    更新日期:2021-01-01
  • Countable zipper fractal interpolation and some elementary aspects of the associated nonlinear zipper fractal operator
    Aequat. Math. (IF 0.851) Pub Date : 2021-01-01
    K. K. Pandey, P. Viswanathan

    This note aims to extend the notion of affine zipper fractal interpolation function from the case of a finite data set to an infinite sequence of data points. We work with a slightly more general setting wherein the assumption of affinity on the functions involved in the construction of the zipper fractal interpolant is dropped. Invoking the iterative functional equation for the countable zipper fractal

    更新日期:2021-01-01
  • A survey on composition operators on some function spaces
    Aequat. Math. (IF 0.851) Pub Date : 2020-12-30
    Emma D’Aniello, Martina Maiuriello

    We investigate some types of composition operators, linear and not, and conditions for some spaces to be mapped into themselves and for the operators to satisfy some good properties.

    更新日期:2020-12-30
  • Symmetric spectral synthesis
    Aequat. Math. (IF 0.851) Pub Date : 2020-12-23
    Eszter Gselmann, László Székelyhidi

    According to the famous and pioneering result of Laurent Schwartz, any closed translation invariant linear space of continuous functions on the reals is synthesizable from its exponential monomials. Due to a result of D. I. Gurevič there is no straightforward extension of this result to higher dimensions. Following Székelyhidi (Acta Math Hungar 153(1):120–142, 2017), with the aid of Gelfand pairs and

    更新日期:2020-12-23
  • The archetypal equation and its solutions attaining the global extremum
    Aequat. Math. (IF 0.851) Pub Date : 2020-12-03
    Mariusz Sudzik

    Let \((\Omega , \mathcal {F}, \mathbb {P})\) be a probability space and let \(\alpha , \beta : \mathcal {F} \rightarrow ~\mathbb {R}\) be random variables. We provide sufficient conditions under which every bounded continuous solution \(\varphi : \mathbb {R} \rightarrow \mathbb {R}\) of the equation \( \varphi (x) = \int _{ \Omega } \varphi \left( \alpha (\omega ) (x-\beta (\omega ))\right) \mathbb

    更新日期:2020-12-03
  • Undirecting membership in models of Anti-Foundation
    Aequat. Math. (IF 0.851) Pub Date : 2020-11-18
    Bea Adam-Day, Peter J. Cameron

    It is known that, if we take a countable model of Zermelo–Fraenkel set theory ZFC and “undirect” the membership relation (that is, make a graph by joining x to y if either \(x\in y\) or \(y\in x\)), we obtain the Erdős–Rényi random graph. The crucial axiom in the proof of this is the Axiom of Foundation; so it is natural to wonder what happens if we delete this axiom, or replace it by an alternative

    更新日期:2020-11-18
  • Characterizations of reverse dynamic weighted Hardy-type inequalities with kernels on time scales
    Aequat. Math. (IF 0.851) Pub Date : 2020-10-29
    S. H. Saker, M. M. Osman, D. O’Regan, R. P. Agarwal

    In this paper, we establish some conditions on nonnegative rd-continuous weight functions \(u\left( x\right) \) and \(\upsilon \left( x\right) \) which ensure that a reverse dynamic inequality of the form $$\begin{aligned} \left( \int _{a}^{\infty }f^{p}(x)\upsilon \left( x\right) \Delta x\right) ^{ \frac{1}{p}}\le C\left( \int _{a}^{\infty }u\left( x\right) \left( \int _{a}^{\sigma \left( x\right)

    更新日期:2020-10-30
  • The chromatic number of triangle-free and broom-free graphs in terms of the number of vertices
    Aequat. Math. (IF 0.851) Pub Date : 2020-10-27
    Naoki Matsumoto, Minako Tanaka

    The Gárfás–Sumner conjecture asks whether for every tree T, the class of (induced) T-free graphs is \(\chi \)-bounded. The conjecture is solved for several special trees, but it is still open in general. Motivated by the conjecture, the chromatic number of triangle-free and broom-free graphs is well studied, since a broom is one of the generalizations of a star, where a broom B(m, n) is the graph obtained

    更新日期:2020-10-30
  • Hyers–Ulam stability of bijective $$\varepsilon $$ ε -isometries between Hausdorff metric spaces of compact convex subsets
    Aequat. Math. (IF 0.851) Pub Date : 2020-10-26
    Yu Zhou, Zihou Zhang, Chunyan Liu

    Let X (resp. Y) be a real Banach space such that the set of all \(w^*\)-exposed points of the closed unit ball \(B(X^*)\) (resp. \(B(Y^*)\)) is \(w^*\)-dense in the unit sphere \(S(X^*)\) (resp. \(S(Y^*)\)), (cc(X), H) (resp. (cc(Y), H)) be the metric space of all nonempty compact convex subsets of X (resp. Y) endowed with the Hausdorff distance H, and \(f:(cc(X),H)\rightarrow (cc(Y),H)\) be a standard

    更新日期:2020-10-30
  • On the balancing property of Matkowski means
    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
  • Transitivity and sensitivity of iterated function systems via Furstenberg families
    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
  • Gradual transitivity in orthogonality spaces of finite rank
    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
  • On the equality of two-variable general functional means
    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
  • A functional equation of tail-balance for continuous signals in the Condorcet Jury Theorem
    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
  • Packing 13 circles in an equilateral triangle
    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
  • On the packing coloring of base-3 Sierpiński graphs and H -graphs
    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
  • Generalized stability of Heisenberg coefficients
    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
  • The weak core inverse
    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
  • Convexity properties of functions defined on metric Abelian groups
    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
  • Wilson’s functional equation with an anti-endomorphism
    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
  • The small dimension lemma and d’Alembert’s equation on semigroups
    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
  • On the Cauchy difference of functions bounded modulo $$\mathbb {Z}$$ Z on “large” sets
    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
  • Continuity of operators intertwining with translation operators on hypergroups
    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
  • Constant diameter and constant width of spherical convex bodies
    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
  • On a linearization of the recursion $$\varvec{U(x_0,x_1,x_2,\ldots )}\varvec{=\varphi (x_0, U(x_1,x_2,\ldots ))}$$ U ( x 0 , x 1 , x 2 , … ) = φ ( x 0 , U ( x 1 , x 2 , … ) ) and its application in economics
    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
  • Some Cauchy mean-type mappings for which the arithmetic mean is invariant
    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
  • A note on the g -angle between subspaces of a normed space
    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
  • Iterative roots of continuous functions and Hyers–Ulam stability
    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
  • On methods for solving composite functional equations
    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
  • Maps stemming from the functional calculus that transform a Kubo–Ando mean into another
    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
  • Computer assisted solution of systems of two variable linear functional equations
    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
  • Characterizations of inner product spaces via angular distances and Cauchy–Schwarz inequality
    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
  • Geometry on the lines of polar spine spaces
    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
  • Hyers–Ulam stability for quantum equations
    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
  • A class of functional equations associated with almost periodic functions
    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
  • Some trigonometric functional equations on monoids generated by their squares
    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
  • A new application of the Gram points. II
    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
  • Bisymmetric functionals revisited or a converse of the Fubini theorem
    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
  • Sections in functional equations
    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
  • On Wigner’s theorem in smooth normed spaces
    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
  • Evolution maps and center manifolds
    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
  • Starshaped sets
    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
  • A fixed point theorem for a system of Pachpatte operator equations
    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
  • On Ulam stability of a third order linear difference equation in Banach spaces
    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
  • Phase-isometries between two $$\ell ^p(\Gamma , H)$$ℓp(Γ,H) -type spaces
    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
  • Packing colorings of subcubic outerplanar graphs
    Aequat. Math. (IF 0.851) Pub Date : 2020-04-28
    Boštjan Brešar,Nicolas Gastineau,Olivier Togni

    Given a graph G and a nondecreasing sequence \(S=(s_1,\ldots ,s_k)\) of positive integers, the mapping \(c:V(G)\longrightarrow \{1,\ldots ,k\}\) is called an S -packing coloring of G if for any two distinct vertices x and y in \(c^{-1}(i)\), the distance between x and y is greater than \(s_i\). The smallest integer k such that there exists a \((1,2,\ldots ,k)\)-packing coloring of a graph G is called

    更新日期:2020-04-28
  • On a certain adaptive method of approximate integration and its stopping criterion
    Aequat. Math. (IF 0.851) Pub Date : 2020-04-17
    Szymon Wąsowicz

    We introduce a new quadrature rule based on Chebyshev’s and Simpson’s rules. The corresponding composite rule induces the adaptive method of approximate integration. We propose a stopping criterion for this method and we prove that if it is satisfied for a function which is either 3-convex or 3-concave, then the integral is approximated with the prescribed tolerance. Nevertheless, we give an example

    更新日期:2020-04-17
  • The shape of planar smooth gestures and the convergence of a gesture recognizer
    Aequat. Math. (IF 0.851) Pub Date : 2020-03-09
    Lorenzo Luzzi,Paolo Roselli

    In this work we provide the mathematical framework of !FTL, a new gesture recognition algorithm. This allows us to algebraically quantify the notion of shape for a smooth planar curve, inspired by the notion of shape of a triangle given previously by Lester in this same journal. In particular, we approximate every gesture, considered as a smooth planar curve, by a polygonal path inscribed on that curve

    更新日期:2020-03-09
  • Angular measures and Birkhoff orthogonality in Minkowski planes.
    Aequat. Math. (IF 0.851) Pub Date : 2020-02-22
    Márton Naszódi,Vilmos Prokaj,Konrad Swanepoel

    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
  • Sandwich results for periodicity and conjugacy
    Aequat. Math. (IF 0.851) Pub Date : 2020-02-17
    Janusz Matkowski,Paweł Wójcik

    Let P be a nonconstant selfmap of a set \(\mathcal {M}\). A sandwich-type theorem for generalized sub- P -periodic functions defined on \(\mathcal {M}\) with values in a reflexive Banach space is proved. In particular, given functions \(f,g:\mathcal {M}\rightarrow \mathbb {R}\), we obtain necessary and sufficient conditions for the existence of a generalized P -periodic function \(F:\mathcal {M}\rightarrow

    更新日期:2020-02-17
  • Approximate n -idempotents and generalized Aluthge transform
    Aequat. Math. (IF 0.851) Pub Date : 2020-02-14
    Mohammad Sal Moslehian

    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
  • The conditional distributivity of nullnorms over uninorms
    Aequat. Math. (IF 0.851) Pub Date : 2020-01-30
    Xiaodong Hou,Gang Li

    The aim of this work is to study the conditional distributivity given by the following functional equation: $$\begin{aligned} F(x,U(y,z))=U(F(x,y),F(x,z)),\ \ x,y,z\in [0,1],\ \ 0 <1 \end{aligned}$$ where F is a nullnorm and U is a uninorm. The paper discusses one case: F is continuous and \(U\in \mathcal {U}_{\max }\) (\(\mathcal {U}_{\min }\)) with continuous underlying operators.

    更新日期:2020-01-30
  • Correction To: Weak limit of iterates of some random-valued functions and its application
    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
  • On the geometric concomitant equation
    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
  • A combinatorial proof for the relation between the exponential function and the logarithmic function
    Aequat. Math. (IF 0.851) Pub Date : 2020-01-21
    Ayaka Ishikawa,Hideaki Morita

    Two combinatorial identities are considered. These identities imply that \(\exp \) and \(\log \) are mutually inverse to one another even in the case where the variable is a noncommutative symbol. The proofs are given by enumeration of permutations and flags in a finite set.

    更新日期:2020-01-21
  • When is a spherical body of constant diameter of constant width?
    Aequat. Math. (IF 0.851) Pub Date : 2020-01-20
    Marek Lassak

    We prove that a smooth convex body of diameter \(\delta < \frac{\pi }{2}\) on the d -dimensional unit sphere \(S^d\) is of constant diameter \(\delta \) if and only if it is of constant width \(\delta \). We also show this equivalence for all convex bodies on \(S^2\). Since, as shown earlier, the equivalence on \(S^d\) is true for every \(\delta \ge \frac{\pi }{2}\), the question whether spherical

    更新日期:2020-01-20
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