Related papers: Coefficient estimates for the class of q-starlike …
In this paper we compare several properties and constructions of the Carlitz polynomials and digit derivatives for continuous functions on $\F_q[[T]].$ In particular, we show a close relation between them as orthonormal bases. Moreover,…
Novel types of convolution operators for quaternion linear canonical transform (QLCT) are proposed. Type one and two are defined in the spatial and QLCT spectral domains, respectively. They are distinct in the quaternion space and are…
This investigation pertains to the construction of a class of generalised deformed derivative operators which furnish the familiar finite difference and the q-derivatives as special cases. The procedure involves the introduction of a linear…
Making use of the Hadamard product(or convolution), we find some estimates on the Taylor-Maclaurin coefficients $|a_{2}|$ and $|a_{3}|$ for functions belong to bi univalent functions of the Bazilevi$\check{c}$ type of order $\gamma$.…
In this paper, we investigate the coefficients of the Taylor expansion of the complex $L$-series of any elliptic curve over $\mathbb{Q}$. We prove that, in the family of quadratic twists by all the discriminants $d$, these coefficients are…
The n-point correlation functions introduced by Bloch and Okounkov have already found several geometric connections and algebraic generalizations. In this Note we formulate a q,t-deformation of this n-point function. The key operator used…
A q-analogue of four dimensional conformally invariant field theory based on the quantum algebra U_{q}(so(4,2)) is proposed. The two- and three-point correlation functions are calculated. The construction is elaborated in order to fit the…
In this paper, we introduce a generalization of the $q$-Meyer-Konig and Zeller operators by means of the $(p,q)$-integers as well as of the $(p,q)$-Gaussian binomial coefficients. For $ 0< q < p <= 1,$ the sequence of the…
We study the convolution function $$ C[f(x)] := \int_1^x f(y)f({x\over y}) {{\rm d} y\over y} $$ when $f(x)$ is a suitable number-theoretic error term. Asymptotics and upper bounds for $C[f(x)]$ are derived from mean square bounds for…
The paper deals with particular classes of $q\times q$ matrix-valued functions which are holomorphic in $\mathbb{C}\setminus[\alpha,+\infty)$, where $\alpha$ is an arbitrary real number. These classes are generalizations of classes of…
The main purpose of this paper is the study of a~new class of summing multilinear operators acting from the product of Banach lattices with some nontrivial lattice convexity. A~mixed Pietsch-Maurey-Rosenthal type factorization theorem for…
Let $E$ be the open unit disk $\{z\in \mathbb{C}: |z|<1\}$. Let $A$ be the class of analytic functions in $E$, which have the form $f(z)=z+a_2z^2+...$. We define operators $L_n^\sigma\colon A\to A$ using the convolution *. Using these…
In this research announcement we present a new q-analog of a classical formula for the exponential generating function of the Eulerian polynomials. The Eulerian polynomials enumerate permutations according to their number of descents or…
We derive in the closed and unimprovable form the bilateral non-asymptotic relations between growth of entire functions and decay rate at infinity of its Taylor coefficients. We investigate the functions of one as well as of several complex…
Let $0 \leq \alpha < n$, $N \in \mathbb{N}$, and let $X$ and $Y$ be ball quasi-Banach function spaces on $\mathbb{R}^n$. We consider operators $T_{\alpha}$ defined by convolution with kernels of type $(\alpha, N)$. Assuming that the powered…
The $q$-analogs of Bernoulli and Euler numbers were introduced by Carlitz. Similar to the recent results on the Hankel determinants for the $q$-Bernoulli numbers established by Chapoton and Zeng, we determine parallel evaluations for the…
In this paper, we determine necessary and sufficient conditions for the generalized Bessel function to be in certain subclasses of starlike and convex functions. Also, we obtain several corollaries as special cases of the main results,…
In this paper, we introduce and investigate a new subclass of the function class $\Sigma$ of bi-univalent functions defined in the open unit disk, which are associated with the S\u{a}l\u{a}gean type $q-$ difference operator and satisfy some…
We study potential operators associated with Laguerre function expansions of convolution and Hermite types, and with Dunkl-Laguerre expansions. We prove qualitatively sharp estimates of the corresponding potential kernels. Then we…
For a fixed polynomial $\Delta$, we study the number of polynomials $f$ of degree $n$ over $\mathbb F_q$ such that $f$ and $f+\Delta$ are both irreducible, an $\mathbb F_q[T]$-analogue of the twin primes problem. In the large-$q$ limit, we…