• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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 • 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 • 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
• 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
• 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
• 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
• 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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