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Received December 15, 2016; Accepted March 18, 2017; Published April 3, 2017
Abstract. In this paper, (p,q)-calculus is applied to construct (p,q)-analogue of divided differences. Another equivalent form of (p,q)-Bernstein operators which generalize the Phillips q-Bernstein polynomials are defined in terms of (p,q)-divided differences. It is shown that these operators reproduce constant as well as linear test functions. Further, we show that the difference of two consecutive (p,q)-Bernstein polynomials of a function f can be expressed in terms of second-order divided differences of f.
How to Cite this Article:
M. Mursaleen, Md. Nasiruzzaman, F. Khan, A. Khan, On (p,q)-analogue of divided differences and Bernstein operators, Journal of Nonlinear Functional Analysis, Vol. 2017 (2017), Article ID 25, pp. 1-13.