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  • Evolution maps and center manifolds
    Aequat. Math. (IF 0.874) 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 0.874) 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 0.874) 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 0.874) 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 0.874) 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
  • Correction To: Weak limit of iterates of some random-valued functions and its application
    Aequat. Math. (IF 0.874) 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 0.874) 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 functional equation on groups with involutions
    Aequat. Math. (IF 0.874) 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
  • A comparison among methods for proving stability
    Aequat. Math. (IF 0.874) 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
  • Fractals for minimalists
    Aequat. Math. (IF 0.874) 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
  • On a class of linear functional equations without range condition
    Aequat. Math. (IF 0.874) 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
  • On a class of abstract convex cone valued functional equations
    Aequat. Math. (IF 0.874) 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
  • Invariant means and iterates of mean-type mappings
    Aequat. Math. (IF 0.874) 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
  • Investigations on the Hyers–Ulam stability of generalized radical functional equations
    Aequat. Math. (IF 0.874) 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
  • More about Wilson’s functional equation
    Aequat. Math. (IF 0.874) Pub Date : 2019-05-27
    Henrik Stetkær

    Let G be a group with an involution \(x \mapsto x^*\), let \(\mu :G \rightarrow \mathbb {C}\) be a multiplicative function such that \(\mu (xx^*) = 1\) for all \(x \in G\), and let the pair \(f,g:G \rightarrow \mathbb {C}\) satisfy that $$\begin{aligned} f(xy) + \mu (y)f(xy^*) = 2f(x)g(y), \ \forall x,y \in G. \end{aligned}$$ For G compact we obtain: If g is abelian, then f is abelian. For G nilpotent

    更新日期:2019-05-27
  • Stochastic processes generating Schur-convex sums
    Aequat. Math. (IF 0.874) Pub Date : 2019-05-27
    Dawid Kotrys, Kazimierz Nikodem

    The notion of Schur-convex stochastic processes is introduced and processes generating Schur-convex sums are investigated. Some inequalities connected with convex stochastic processes are obtained. A counterpart of the result of Ng stating that a stochastic process generates Schur-convex sums if and only if it is Wright-convex is proved.

    更新日期:2019-05-27
  • Weak limit of iterates of some random-valued functions and its application
    Aequat. Math. (IF 0.874) Pub Date : 2019-04-05
    Karol Baron

    Given a probability space \( (\Omega , {\mathcal {A}}, P) \), a complete and separable metric space X with the \( \sigma \)-algebra \( {\mathcal {B}} \) of all its Borel subsets, a \( {\mathcal {B}} \otimes {\mathcal {A}} \)-measurable and contractive in mean \( f: X \times \Omega \rightarrow X \), and a Lipschitz F mapping X into a separable Banach space Y we characterize the solvability of the equation

    更新日期:2019-04-05
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