Approximation properties of modified q-Bernstein-Kantorovich operators

Authors : Ana Maria ACU, Purshottam AGRAWAL, Dharmendra KUMAR

Pages : 2170-2197

Doi:10.31801/cfsuasmas.545460

View : 8 | Download : 9

Publication Date : 2019-08-01

Article Type : Research Paper

Abstract :In the present paper we define a q-analogue of the modified Bernstein-Kantorovich operators introduced by Ozarslan and Duman insert ignore into journalissuearticles values(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 insert ignore into journalissuearticles values(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