Related papers: Bernstein polynomials on Simplex
In this work, we derive numerous identities for multivariate q-Euler polynomials by using umbral calculus.
We consider a sequence of composite Bernstein operators and the quadrature formulae associated with them. Upper bounds for the approximation error of continuous functions and for the approximation of integrals of continuous functions are…
This note gives a simple approach to q-analogues of some results associated with Abel polynomials.
A systematic procedure for generating certain identities involving elementary symmetric functions is proposed. These identities, as particular cases, lead to new identities for binomial and q-binomial coefficients.
We prove an analogue of the classical Bernstein polynomial inequality on a compact subset $E$ of the real line. The Lipschitz continuity of the Green function for the complement of $E$ with respect to the extended complex plane and the…
We prove limit relations between the sharp constants in the multivariate Bernstein-Nikolskii type inequalities for trigonometric polynomials and entire functions of exponential type with the spectrum in a centrally symmetric convex body.
This paper describes a novel method to approximate the polynomial coefficients of regression functions, with particular interest on multi-dimensional classification. The derivation is simple, and offers a fast, robust classification…
Transformation formulas for four-parameter refinements of the q-trinomial coefficients are proven. The iterative nature of these transformations allows for the easy derivation of several infinite series of q-trinomial identities, and can be…
Tensor polynomial identities generalize the concept of polynomial identities on $d \times d$ matrices to identities on tensor product spaces. Here we completely characterize a certain class of tensor polynomial identities in terms of their…
We show that given an ideal I generated by regular functions f_1,...,f_r on the smooth complex variety X, the Bernstein-Sato polynomial of I is equal to the reduced Bernstein-Sato polynomial of the function g=\sum_{i=1}^rf_iy_i on the…
In this paper we compute b-functions (or Bernstein-Sato polynomials) of various semi-invariants of quivers. The main tool is an explicit relation for the b-functions between semi-invariants that correspond to each other under reflection…
We present an elementary self-contained folkloristic proof, using limits of primitives of Bernstein polynomials, for the existence of primitive functions of continuous functions defined on the unit interval.
We prove a four dimensional version of the Bernstein Theorem, with complex polynomials being replaced by quaternionic polynomials. We deduce from the theorem a quaternionic Bernstein's inequality and give a formulation of this last result…
Recently, Mursaleen et al applied (p,q)-calculus in approximation theory and introduced (p,q)-analogue of Bernstein operators in [16]. In this paper, we construct and introduce a generalization of the bivariate Bleimann-Butzer-Hahn…
We show that integrating a polynomial of degree t on an arbitrary simplex (with respect to Lebesgue measure) reduces to evaluating t homogeneous polynomials of degree j = 1, 2,. .. , t, each at a unique point $\xi$ j of the simplex. This…
In this paper we introduce three combinatorial models for symmetrized poly-Bernoulli numbers. Based on our models we derive generalizations of some identities for poly-Bernoulli numbers. Finally, we set open questions and directions of…
We show that on separable Banach spaces admitting a separating polynomial, any uniformly continuous, bounded, real-valued function can be uniformly approximated by Lipschitz, analytic maps on bounded sets.
An extension to triangular domains of the univariate q-Bernstein basis functions is introduced and analyzed. Some recurrence relations and properties such as partition of unity and degree elevation are proved for them. It is also proved…
We introduce two q-analogues of the 2D-Hermite polynomials which are functions of two complex variables. We derive explicit formulas, orthogonality relations, raising and lowering operator relations, generating functions, and Rodrigues…
We find new bi-Lipschitz invariants for functions of two complex variables.