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Lacunary statistical convergence of Bernstein operator sequences
(INST ADVANCED SCIENCE EXTENSION, 2017-11)
The Bernstein operator is one of the important topics of approximation theory in which it has been studied in great details for a long time. Recently the statistical convergence of Bernstein operators was studied. In this ...
Summation formulas for the products of the Frobenius-Euler polynomials
(SPRINGER, 2017-10)
We present here a further investigation for the classical Frobenius-Euler polynomials. By making use of the generating function methods and summation transform techniques, we establish some summation formulas for the ...
A novel approach for obtaining new identities for the lambda extension of q- Euler polynomials arising from the q-umbral calculus
(INT SCIENTIFIC RESEARCH PUBLICATIONS, 2017)
In this article, a new q-generalization of the Apostol-Euler polynomials is introduced using the usual q-exponential function. We make use of such a generalization to derive several properties arising from the q-umbral ...
Szasz-Durrmeyer operators involving Boas-Buck polynomials of blending type
(SPRINGER INTERNATIONAL PUBLISHING A, 2017-05-23)
The present paper introduces the Szasz-Durrmeyer type operators based on Boas-Buck type polynomials which include Brenke type polynomials, Sheffer polynomials and Appell polynomials considered by Sucu et al. (Abstr. Appl. ...
On an Analogue of Euler Polynomials and Related to Extended Fermionic p-Adic Integrals on Z(p)
(SPRINGER INTERNATIONAL PUBLISHING AG, 2017-09)
In the paper, using the extended fermionic p-adic integral on Z(p), the authors find some applications of the umbral calculus. From these applications, the authors derive some identities on the weighted Euler numbers and ...
Blending type approximation by Stancu-Kantorovich operators based on Polya-Eggenberger distribution
(DE GRUYTER OPEN LTD, 2017)
In the paper the authors introduce the Kantorovich variant of Stancu operators based on Polya-Eggenberger distribution. By making use of this new operator, we obtain some indispensable auxiliary results. We also deal with ...
Rate of convergence by Kantorovich-Szasz type operators based on Brenke type polynomials
(SPRINGEROPEN, 2017-06-29)
The present paper deals with the approximation properties of the univariate operators which are the generalization of the Kantorovich-Szasz type operators involving Brenke type polynomials. We investigate the order of ...
Linking of Bernstein-Chlodowsky and Szasz-Appell-Kantorovich type operators
(INT SCIENTIFIC RESEARCH PUBLICATIONS, 2017)
In the present paper, we define a sequence of bivariate operators by linking the Bernstein-Chlodowsky operators and the Szasz-Kantorovich operators based on Appell polynomials. First, we establish the moments of the operators ...
(ρ,q)-Volkenborn integration
(ACADEMIC PRESS INC ELSEVIER SCIENCE, 2017-02)
In the paper, we introduce an analogue of Haar distribution based on (rho, q)-numbers, as follows:
mu(rho,q) (a + p(N)Z(p)) = rho(pN)/[p(N)](rho,q) (q/rho)(a)
By means of this distribution, we derive (rho, q)-analogue ...
lambda-STATISTICAL CONVERGENCE OF BERNSTEIN POLYNOMIAL SEQUENCES
(MILI PUBL, 2017-01)
The Bernstein operator is one of the important topics of approximation theory in which it has been studied in great details for a long time. The aim of this paper is to study the lambda-statistical convergence of sequence ...
