Approximation properties of modified q-Bernstein-Kantorovich operators
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Date
2019-08-01
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Ankara Üniversitesi Fen Fakültesi
Abstract
In the present paper we define a q-analogue of the modified Bernstein-Kantorovich operators
introduced by Ozarslan and Duman (Numer. Funct. Anal. Optim. 37:92-105,2016). We establish
the shape preserving properties of these operators e.g. monotonicity and convexity and study the rate
of convergence by means of Lipschitz class and Peetre's K-functional and degree of approximation with
the aid of a smoothing process e.g Steklov mean. Further, we introduce the bivariate case of modified
q-Bernstein-Kantorovich operators and study the degree of approximation in terms of the partial and
total modulus of continuity and Peetre's K-functional. Finally, we introduce the associated GBS (Generalized
Boolean Sum) operators and investigate the approximation of the Bogel continuous and Bogel
differentiable functions by using the mixed modulus of smoothness and Lipschitz class.
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Keywords
Peetre's K-functional, Modulus of continuity, Lipschitz class