Related papers: Uniform limits of $\mathcal B_1^{**}$-functions

For an analytic function $f(z)$ on the unit disk $|z|<1$ with $f(0)=f'(0)-1=0$ and $f(z)\ne0, 0<|z|<1,$ we consider the power deformation $f_c(z)=z(f(z)/z)^c$ for a complex number $c.$ We determine those values $c$ for which the operator…

For nonuniform exponentially bounded evolution families defined on Banach spaces, we introduce a class of Banach function spaces, whose norms are completely determined by the nonuniform behaviour of the corresponding evolution family. We…

Assuming that $S$ is the space of functions of regular variation, $\omega\in S$, $0< p<\infty$, a function $f$ holomorphic in $B^n$ is said to be of Besov space $B_p(\omega)$ if $$\|f\|^p_{B_p(\omega )}=\int_{B^n}…

In this paper we study various types of spectra of functions $\phi:\jj\to X$, where $\jj\in\{\r_+,\r\}$ and $X$ is a complex Banach space. We show that uniform spectrum defined in [15] coincides with Carleman spectrum for $\phi\in…

In this paper, we introduced some notions on the n-Normed Spaces. Those are bounded k-linear (or multilinear) functionals and k-continuous (or multicontinuous) functions with k \in \mathbb{N}. We defined k-linear functionals under several…

Let M and N be Orlicz functions. We establish some combinatorial inequalities and show that the product spaces l^n_M(l^n_N) are uniformly isomorphic to subspaces of L_1 if M and N are "separated" by a function t^r, 1<r<2.

We completely characterize the unimodal category for functions $f:\mathbb R\to[0,\infty)$ using a decomposition theorem obtained by generalizing the sweeping algorithm of Baryshnikov and Ghrist. We also give a characterization of the…

For a domain $\Omega\subset\mathbb R^n$, we introduce the concept of a uniformly $C^m$ defining function. We characterize uniformly $C^m$ defining functions in terms of the signed distance function for the boundary and provide a large class…

We introduce the notion of $B_1$-retract and investigate the connection between $B_1$- and $H_1$-retracts.

In this paper, we will see that the Cartesian product of two 2-Banach spaces is also 2-Banach space and discuss some properties of closed linear operator in linear 2-normed space. We also describe the concept of different types of…

The canonical theory of $N=1$ supergravity is applied to Bianchi class A spatially homogeneous cosmologies. The full set of quantum constraints are then solved with the possible ordering ambiguity taken into account by introducing a free…

The first-order Euler-Maclaurin formula relates the sum of the values of a smooth function on an interval of integers with its integral on the same interval on $\mathbb R$. We formulate here the analogue for functions that are just of…

In this paper, we define certain subclass of harmonic univalent function in the unit disc U = {z in C :|z|<1} by using q-differential operator. Also we obtain coefficient inequalities, growth and distortion theorems for this subclass.

In this article, we study certain transcendental function spaces arising in potential theory within the framework of Orlicz spaces. Specifically, we generalize Bessel and Lizorkin-Triebel spaces to the nonstandard setting of Orlicz spaces.…

A plethora of spaces in Functional Analysis (Braun-Meise-Taylor and Carleman ultradifferentiable and ultraholomorphic classes; Orlicz, Besov, Lipschitz, Lebesque spaces, to cite the main ones) are defined by means of a weighted structure,…

The Euclidean division of two formal series in one variable produces a sequence of series that we obtain explicitly, remarking that the case where one of the two initial series is 1 is sufficiently generic. As an application, we define a…

There have been, over the last 8 years, a number of far reaching extensions of the famous original F. and M. Riesz's uniqueness theorem that states that if a bounded analytic function in the unit disc of the complex plane $\Bbb C$ has the…

In this paper we show that, using combinatorial inequalities and Matrix-Averages, we can generate Musielak-Orlicz spaces, i.e., we prove that $1/\pi \sum_{\pi} \max\limits_{1 \leq i \leq n} \abs{x_i y_{i\pi(i)}} \sim \norm{x}_{\Sigma M_i}$,…

In the paper it is shown that there exist a function g from L1[0,1] and a weight function 0<u(x)<=1, so that g is universal for each classes L^p_u[0,1], p>= 1 with respect to signs-subseries of its Fourier-Walsh series.

The paper is concerned with b-metric and generalized b-metric spaces. One proves the existence of the completion of a generalized b-metric space and some fixed point results. The behavior of Lipschitz functions on b-metric spaces of…