Related papers: On Bernstein-type theorems

Particular solutions of the Benney equations are constructed. Their properties are discussed.

A multidimensional generalization of the Bernstein class of functions and the properties of functions of the introduced class are examined. In particular, a new proof of the integral representation of Bernstein functions of many variables…

In this work we state a Theorem on number theory and apply it to solve some ordinary and partial differential equations.

In this paper, we gave some properties of binomial coefficient.

We investigate splitting-type variational problems with some linear growth conditions. For balanced solutions of the associated Euler-Lagrange equation we receive a result analogous to Bernstein's theorem on non-parametric minimal surfaces.…

In this paper we obtain a Bernstein type inequality for a class of weakly dependent and bounded random variables. The proofs lead to a moderate deviations principle for sums of bounded random variables with exponential decay of the strong…

We give a distribution-dependent concentration inequality for functions of independent variables. The result extends Bernstein's inequality from sums to more general functions, whose variation in any argument does not depend too much on the…

New differential-recurrence properties of dual Bernstein polynomials are given which follow from relations between dual Bernstein and orthogonal Hahn and Jacobi polynomials. Using these results, a fourth-order differential equation…

We obtain some results related to Romanoff's theorem.

In this paper we investigate some properties for the q-Euler numbers ans polymials. From these properties we give some identities on the Bernstein polymials and q-Euler polynpmials.

In this paper, we investigate the properties of q-Hermite polynomials related to q-Bernstein polynomials. From these properties, we derive some interesting relations between q-Berstein polynomials and q-Hermite polynomials.

In this paper we constructed new q-extension of Bernstein polynomials. Fron those q-Berstein polynomials, we give some interesting properties and we investigate some applications related this q-Bernstein polynomials.

We introduce a new type of Bernstein operators, which can be used to approximate the functions with inner singularities. The direct and inverse results of the weighted approximation of this new type of combinations are given.

We obtain some new inequalities of Chebyshev Type.

We formulate and discuss a conjecture which would extend a classical inequality of Bernstein.

We give direct and inverse theorems for the weighted approximation of functions with inner singularities by combinations of Bernstein polynomials.

We investigate some interesting properties of Bernstein polynomials associated with boson p-adic integrals on Zp.

We prove several theorems concerning arithmetic properties of Stern polynomials defined in the following way: $B_{0}(t)=0, B_{1}(t)=1, B_{2n}(t)=tB_{n}(t)$, and $B_{2n+1}(t)=B_{n}(t)+B_{n+1}(t)$. We study also the sequence…

We obtain similar types of conclusions as that of Br\"{u}ck [1] for two differential polynomials which in turn radically improve and generalize several existing results. Moreover, a number of examples have been exhibited to justify the…

We derive an expression for the generalized Bernoulli numbers in terms of the Bernoulli numbers involving the (exponential) complete Bell polynomials.