Related papers: $q$-Bernstein functions and applications
In this paper, we consider the degenerate Carlitz q-Bernoulli numbers and polynomials and we investigate some properties of those polynomials.
We use the Laplace transform and the Gamma function to introduce a new integral transform and name it the Laplace-type transform possessing the property of mapping a function to a functional sequence, which cannot be achieved by the Laplace…
In this paper, we study some properties such as the monotonicity, logarithmically complete monotonicity, logarithmic convexity, and geometric convexity, of the combinations of gamma function and power function. The results we obtain…
We study three different $q$-analogues of the harmonic numbers. As applications, we present some generating functions involving number theoretical functions and give the $q$-generalization of Gosper's exponential generating function of…
We compute Fourier transforms of functions expressed as a ratio of one of the Jacobi elliptic functions divided by $\sinh(\pi x)$ or $\cosh(\pi x)$. In many cases, the resulting Fourier transform remains within the same class of functions.…
Extending earlier work by Rogers, Wiener-Hopf factorisation is studied for a class of functions closely related to Nevanlinna-Pick functions and complete Bernstein functions. The name 'Rogers functions' is proposed for this class. Under…
The aim of this paper is to present the new results concerning some functionals of Brownian motion with drift and present their applications in financial mathematics. We find a probabilistic representation of the Laplace transform of…
In this paper we study (h,q)-zeta functions associated with (h,q)-Bernoulli numbers and polynomials.
We prove two identities for multivariate Bernstein polynomials on simplex, which are considered on a pointwise. In this paper, we study good approximations of Bernstein polynomials for every continuous functions on simplex and the higher…
A form of the Laplace transform is reviewed as a paradigm for an entire class of fractional functional transforms. Various of its properties are discussed. Such transformations should be useful in application to differential/integral…
We establish a series of integral formulae involving the Hurwitz zeta function. Applications are given to integrals of Bernoulli polynomials, log Gamma(q) and log sin(q).
We obtain eigenvalues and eigenvectors of the $(\alpha,q)$-Bernstein operator $T_{n,q,\alpha}$. Moreover, we will give the limit behaviour of these eigenvalues and eigenvectors for all $q.$
The Laplace transform in Komatsu ultradistributions is considered. Also, conditions are given under which an analytic function is a Laplace transformation of an ultradistribution.
We introduce here the q-Laplace transform as a new weapon in Tsallis' arsenal, discussing its main properties and analyzing some examples. The q-Gaussian instance receives special consideration. Also, we derive the q-partition function from…
We present a deformed algebra related to the q-exponential and the q-logarithm functions that emerge from nonextensive statistical mechanics. We also develop a q-derivative (and consistently a q-integral) for which the q-exponential is an…
In this paper we show how the superquadratic functions can be used as a tool for researching other types of convex functions like $\phi $-convexity, strong-convexity and uniform convexity. We show how to use inequalities satisfied by…
In the paper, we investigate the uniqueness problem of entire functions concerning their linear differential polynomial in shift and obtain three results which improve and generalize the recent result due to Qi (Ann. Polon. Math., 102…
We consider the $q$th root number function for the symmetric group. Our aim is to develop an asymptotic formula for the multiplicities of the $q$th root number function as $q$ tends to $\infty$. We use character theory, number theory and…
In this paper, First we have given the modified form of (p,q)-analogues of Bernstein and Bernstein operators [21-23] and then we introduce a new analogue of Bernstein-Kantorovich operators which we call as (p,q)-Bernstein-Kantorovich…
We prove that every completely monotone function defined on a right-unbounded open interval admits a Newton series expansion at every point of that interval. This result can be viewed as an analog of Bernstein's little theorem for…