Approximation properties of modified q-Bernstein-Kantorovich operators

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.

Keywords

• Peetre's K-functional,modulus of continuity,Lipschitz class,Bogel continuous,Bogel differentiable,GBS operators

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