q-Bernstein-Type Polynomials for Functions of Two Variables with Their Generating and Interpolation Functions

Mehmet ACIKGOZ¹, Erdoğan ŞEN² and Serkan ARACI^3,

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

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

Abstract

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.

Keywords:
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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