Let U be an open subset of \(\mathbb {C}\) with boundary point \(x_0\) and let \(A_{\alpha }(U)\) the space functions analytic on that belong to lip\(\alpha (U)\), “little Lipschitz class”. We consider condition \(S= \sum _{n=1}^{\infty }2^{(t+\lambda +1)n}M_*^{1+\alpha }(A_n \setminus U)< \infty ,\) where t is a non-negative integer, \(0<\lambda <1\), \(M_*^{1+\alpha }\) lower \(1+\alpha \) di...

Let $ H$ be a Hilbert space and $C$ be a closed, convex and nonempty subset of $H$. Let $T:C rightarrow H$ be a non-self and non-expansive mapping. V. Colao and G. Marino with particular choice of the sequence  ${alpha_{n}}$ in Krasonselskii-Mann algorithm, ${x}_{n+1}={alpha}_{n}{x}_{n}+(1-{alpha}_{n})T({x}_{n}),$ proved both weak and strong converging results. In this paper, we generalize thei...

We construct a quantum searching model of signed edge driven by walk. The time evolution operator this walk provides weighted adjacency matrix induced the assignment sign to each edge. This can be regarded as so-called coloring. Then an application, under arbitrary coloring which gives matching on complete graph $$n+1$$ vertices we consider search colored from set graph. show that finds within...

Given $$m, n, q\in \mathbb {N}$$ such that q is a prime power and $$m\ge 3$$ , $$a\in {F}_q$$ we establish sufficient condition for the existence of primitive pair $$(\alpha f(\alpha ))$$ in $$\mathbb {F}_{q^m}$$ $$\alpha $$ normal over $$\text {Tr}_{\mathbb {F}_{q^m}/\mathbb {F}_q}(\alpha ^{-1})=a$$ where $$f(x)\in {F}_{q^m}(x)$$ rational function degree sum n. Further, when $$n=2$$ $$q=5^k$$ ...

Let $$p\in [1,\infty ]$$ , $$q\in )$$ $$s\in \mathbb {Z}_+:=\mathbb {N}\cup \{0\}$$ $$\alpha \in {R}$$ and $$\beta (0,1)$$ . In this article, the authors first find a reasonable version $$\widetilde{I}_{\beta }$$ of (generalized) fractional integral $$I_{\beta on special John–Nirenberg–Campanato space via congruent cubes, $$JN_{(p,q,s)_{\alpha }}^{\textrm{con}}(\mathbb {R}^n)$$ which coincides ...

The Bernstein-Szegő inequality for the Weyl derivative of real order $\alpha\ge 0$ trigonometric polynomials degree $n$ is considered. aim to find values parameters which sharp constant in this equal $n^\alpha$ (the classical value) all $L_p$-spaces, $0\le p\le\infty$. set such $\alpha$ described some important particular cases Weyl-Szegő derivative, namely, Riesz and conjugate $n\in\mathbb N$....

We prove an analogue of Lang's conjecture on divisible groups for polynomial dynamical systems over number fields. In our setting, the role group is taken by small orbit a point $\alpha$ where $f$ given \begin{align*} \mathcal{S}_\alpha = \{\beta \in \mathbb{C}; f^{\circ n}(\beta) n}(\alpha) \text{ some } n \mathbb{Z}_{\geq 0}\}. \end{align*} Our main theorem classification algebraic relations ...