1,530 research outputs found
On The Properties Of -Bernstein-Type Polynomials
The aim of this paper is to give a new approach to modified -Bernstein
polynomials for functions of several variables. By using these polynomials, the
recurrence formulas and some new interesting identities related to the second
Stirling numbers and generalized Bernoulli polynomials are derived. Moreover,
the generating function, interpolation function of these polynomials of several
variables and also the derivatives of these polynomials and their generating
function are given. Finally, we get new interesting identities of modified
-Bernoulli numbers and -Euler numbers applying -adic -integral
representation on and -adic fermionic -invariant integral
on , respectively, to the inverse of -Bernstein polynomials.Comment: 17 pages, some theorems added to new versio
The Evaluation of the Sums of More General Series by Bernstein Polynomials
Let n,k be the positive integers, and let S_{k}(n) be the sums of the k-th
power of positive integers up to n. By means of that we consider the evaluation
of the sum of more general series by Bernstein polynomials. Additionally we
show the reality of our idea with some examples.Comment: 6 pages, submitte
A note on q-Bernstein 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.Comment: 13 page
A note on the values of the weighted q-Bernstein polynomials and modified q-Genocchi numbers with weight alpha and beta via the p-adic q-integral on Zp
The rapid development of q-calculus has led to the discovery of new
generalizations of Bernstein polynomials and Genocchi polynomials involving
q-integers. The present paper deals with weighted q-Bernstein polynomials and
q-Genocchi numbers with weight alpha and beta. We apply the method of
generating function and p-adic q-integral representation on Zp, which are
exploited to derive further classes of Bernstein polynomials and q-Genocchi
numbers and polynomials. To be more precise we summarize our results as
follows, we obtain some combinatorial relations between q-Genocchi numbers and
polynomials with weight alpha and beta. Furthermore, we derive an integral
representation of weighted q-Bernstein polynomials of degree n on Zp. Also we
deduce a fermionic p-adic q-integral representation of product weighted
q-Bernstein polynomials of different degrees n1,n2,...on Zp and show that it
can be written with q-Genocchi numbers with weight alpha and beta which yields
a deeper insight into the effectiveness of this type of generalizations. Our
new generating function possess a number of interesting properties which we
state in this paper.Comment: 10 page
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