For $l$-homogeneous linear differential operators $\mathcal{A}$ of constant rank, we study the implication $v_j\rightharpoonup v$ in $X$ and $\mathcal{A} v_j\rightarrow \mathcal{A} $W^{-l}Y$ implies $F(v_j)\rightsquigarrow F(v)$ $Z$, where $F$ is an $\mathcal{A}$-quasiaffine function $\rightsquigarrow$ denotes appropriate type weak convergence. Here $Z$ a local $L^1$-type space, either space $\...

Let $${{\mathcal {F}}}_n$$ be the Farey series of order $$n\ge 1$$ . We obtain sharp effective estimates sums $$\begin{aligned} F_n(f)= \sum _{\frac{{\kappa }}{{\lambda }}\in {{\mathcal {F}}}_n} f\Big (\frac{{\kappa }}\Big ),{\qquad }F_{n,{\sigma }}(f)= \frac{1}{{\kappa }^{\sigma }{\lambda }}f\Big }0< {\sigma }\le 1, \end{aligned}$$ for 1-periodic functions f satisfying weak local regularity as...

Abstract Let $k\geq 2$ be an integer. We prove that the 2-automatic sequence of odious numbers $\mathcal {O}$ is a k -additive uniqueness set for multiplicative functions: if function f satisfies multivariate Cauchy’s functional equation $f(x_1+x_2+\cdots +x_k)=f(x_1)+f(x_2)+\cdots +f(x_k)$ arbitrary $x_1,\ldots ,x_k\in \mathcal , then identity $f(n)=n$ all $n\in \mathbb {N}$ .

Let G be a graph embedded in surface and let the set of all faces G. For given subset $$\mathcal F$$ even (faces bounded by an cycle), resonance with respect to $${\mathcal {F}}$$ , denoted $$R(G;\mathcal F)$$ is such that its vertex perfect matchings two vertices $$M_1$$ $$M_2$$ are adjacent if only symmetric difference $$M_1\oplus M_2$$ cycle bounding some face . It has been shown plane eleme...

In the present paper, Radial Basis Function interpolations are applied to approximate a fuzzy function $tilde{f}:Rrightarrow mathcal{F}(R)$, on a discrete point set $X={x_1,x_2,ldots,x_n}$, by a fuzzy-valued function $tilde{S}$. RBFs are based on linear combinations of terms which include a single univariate function. Applying RBF to approximate a fuzzy function, a linear system wil...

Our aim in this article is to contribute the theory of Lipschitz free p-spaces for $$0<p\le 1$$ over Euclidean spaces $${\mathbb{R}}^d$$ and $${\mathbb{Z}}^d$$ . To that end, we show $${\mathcal{F}}_p({\mathbb{R}}^d)$$ admits a Schauder basis every $$p\in (0,1]$$ , thus generalizing corresponding result case $$p=1$$ by Hájek Pernecká (J Math Anal Appl 416(2):629–646, 2014, Theorem 3.1) answerin...

the idea of difference sequences of real (or complex) numbers was introducedby ki zmaz cite{kizmaz}. in this paper, using the difference operator and alacunary sequence, we introduce and examine the class of sequence $bv_{theta}left(  delta,mathcal{f}right)  .$ we study some of its properties likesolidity, symmetricity, etc.