Turkish Journal of Analysis and Number Theory
ISSN (Print): 2333-1100 ISSN (Online): 2333-1232 Website: http://www.sciepub.com/journal/tjant
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Turkish Journal of Analysis and Number Theory. 2013, 1(1), 36-42
DOI: 10.12691/tjant-1-1-8
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q-Bernstein-Type Polynomials for Functions of Two Variables with Their Generating and Interpolation Functions

Mehmet ACIKGOZ1, Erdoğan ŞEN2 and Serkan ARACI3,

1University of Gaziantep, Faculty of Arts and Science, Department of Mathematics, Gaziantep, Turkey

2Department of Mathematics, Faculty of Science and Letters, Namik Kemal University, Tekirdağ, Turkey

3Atatürk Street, Hatay, Turkey

Pub. Date: November 04, 2013

Cite this paper:
Mehmet ACIKGOZ, Erdoğan ŞEN and Serkan ARACI. q-Bernstein-Type Polynomials for Functions of Two Variables with Their Generating and Interpolation Functions. Turkish Journal of Analysis and Number Theory. 2013; 1(1):36-42. doi: 10.12691/tjant-1-1-8


The aim of this paper is to give a new approach to modified q-Bernstein polynomials for functions of two variables. By using these type polynomials, we derive recurrence formulas and some new interesting identities related to the second kind Stirling numbers and generalized Bernoulli polynomials. Moreover, we give the generating function and interpolation function of these modified q-Bernstein polynomials of two variables and also give the derivatives of these polynomials and their generating function.

generating function Bernstein polynomial of two variables Bernstein operator of two variables shift difference operator q-difference operator second kind Stirling numbers generalized Bernoulli polynomials Mellin transformation interpolation function

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