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Nazim I. Mahmudov

Publications and source records attributed to Nazim I. Mahmudov.

44 records · Page 3Linked to original sources
arXiv2015

A $q$-Umbral Approach to $q$-Appell Polynomials

In this paper we aim to specify some characteristics of the so called family of $q$-Appell Polynomials by using $q$-Umbral calculus. Next in our study, we focus on $q$-Genocchi numbers and polynomials as a famous member of this family. To do this, firstly we show that any arbitrary polynomial can be written based on a linear combination of $q$-Genocchi polynomials. Finally, we approach to the point that similar properties can be found for the other members of the class of $q$-Appell polynomials.

math.NT↗
arXiv2014

Difference equations of q-Appell polynomials

In this paper, we study some properties of the q-Appell polynomials, including the recurrence relations and the q-difference equations which extend some known calssical (q=1) results. We also provide the recurrence relations and the q-difference equations for q-Bernoulli polynomials, q-Euler polynomials, q-Genocchi polynomials and for newly defined q-Hermite polynomials, as special cases of q-Appell polynomials

math.CA↗
arXiv2014

Approximation by Genuine $q$-Bernstein-Durrmeyer Polynomials in Compact Disks in the case $q > 1$

This paper deals with approximating properties of the newly defined $q$-generalization of the genuine Bernstein-Durrmeyer polynomials in the case $q>1$, whcih are no longer positive linear operators on $C[0,1]$. Quantitative estimates of the convergence, the Voronovskaja type theorem and saturation of convergence for complex genuine $q$-Bernstein-Durrmeyer polynomials attached to analytic functions in compact disks are given. In particular, it is proved that for functions analytic in $\left\{ z\in\mathbb{C}:\left\vert z\right\vert q,$ the rate of approximation by the genuine $q$-Bernstein-Durrmeyer polynomials ($q>1$) is of order $q^{-n}$ versus $1/n$ for the classical genuine Bernstein-Durrmeyer polynomials. We give explicit formulas of Voronovskaja type for the genuine $q$-Bernstein-Durrmeyer for $q>1$.

math.AP↗
arXiv2012

A new class of generalized Genocchi polynomials

The main purpose of this paper is to introduce and investigate a new class of generalized Genocchi polynomials based on the q-integers. The q-analogues of well-known formulas are derived. The q-analogue of the Srivastava--Pintér addition theorem is obtained.

math.CA↗
arXiv2012

A new class of generalized Bernoulli polynomials and Euler polynomials

The main purpose of this paper is to introduce and investigate a new class of generalized Bernoulli polynomials and Euler polynomials based on the q-integers. The q-analogues of well-known formulas are derived. The q-analogue of the Srivastava--Pintér addition theorem is obtained. We give new identities involving q-Bernstein polynomials.

math.CA↗
arXiv2011

Korovkin type theorem for iterates of certain positive linear operators

In this paper we prove that if T:C[0,1] \rightarrow C[0,1] is a positive linear operator with T(e_0)=1 and T(e_1)-e_1 does not change the sign, then the iterates T^{m} converges to some positive linear operator T^{\infty} :C[0,1] \rightarrow C[0,1] and we derive quantitative estimates in terms of modulii of smoothness. This result enlarges the class of operators for which the limit of the iterates can be computed and the quantitative estimates of iterates can be given.

math.FA↗
arXiv2010

Approximation by q-Szasz operators

his paper deals with approximating properties of the newly defined $q$-generalization of the Szász operators in the case $q>1$. Quantitative estimates of the convergence in the polynomial weighted spaces and the Voronovskaja's theorem are given. In particular, it is proved that the rate of approximation by the $q$-Szász operators ($q>1$) is of order $q^{-n}$ versus $1/n$ for the classical Szász--Mirakjan operators.

math.FA↗