Approximating B-continuous functions using GBS operators of Bernstein–Schurer–Stancu type based on q-integers

“…Several researchers have made significant contributions to this area of approximation theory (cf. [20][21][22][23][24][25][26][27][28][29] exists and is finite. The limit is said to be the B-differential of f at the point .x 0 , y 0 / and is denoted by D B .f ; x 0 , y 0 /, and the space of all B-differentiable functions is denoted by D b .X Y/.…”

Section: Construction Of Gbs Operator Of Q-bernstein-schurer-kantorovmentioning

confidence: 99%

Kantorovich variant of a new kind of q‐Bernstein–Schurer operators

Ruchi

İspir

Agrawal

2017

Math Methods in App Sciences

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Ren and Zeng (2013) introduced a new kind of q‐Bernstein–Schurer operators and studied some approximation properties. Acu et al. (2016) defined the Durrmeyer modification of these operators and studied the rate of convergence and statistical approximation. The purpose of this paper is to introduce a Kantorovich modification of these operators by using q‐Riemann integral and investigate the rate of convergence by means of the Lipschitz class and the Peetre's K‐functional. Next, we introduce the bivariate case of q‐Bernstein–Schurer–Kantorovich operators and study the degree of approximation with the aid of the partial modulus continuity, Lipschitz space, and the Peetre's K‐functional. Finally, we define the generalized Boolean sum operators of the q‐Bernstein–Schurer–Kantorovich type and investigate the approximation of the Bögel continuous and Bögel differentiable functions by using the mixed modulus of smoothness. Furthermore, we illustrate the convergence of the operators considered in the paper for the univariate case and the associated generalized Boolean sum operators to certain functions by means of graphics using Maple algorithms. Copyright © 2017 John Wiley & Sons, Ltd.

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“…Acu and Muraru proposed two dimensional Bernstein‐Schurer‐Kantorovich operators involving q ‐integers and established some approximation theorems of these operators. For some related articles in this arena, we refer the reader to (cf other studies() etc).…”

Section: Introductionmentioning

confidence: 99%

Generalized Bernstein‐Kantorovich–type operators on a triangle

Kajla

2019

Math Methods in App Sciences

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In this note, we construct generalized Bernstein‐Kantorovich–type operators on a triangle. The concern of this note is to present a Voronovskaja‐type and Grüss Voronovskaja‐type asymptotic theorems, and some estimates of the rate of approximation with the help of K‐functional, first and second order modulus of continuity. We also obtain Korovkin‐ and Voronovskaja‐type statistical approximation theorems via weighted mean matrix method. Lastly, we show that the numerical results which explain the validity of the theoretical results and the effectiveness of the constructed operators.

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Approximating B-continuous functions using GBS operators of Bernstein–Schurer–Stancu type based on q-integers

Cited by 22 publications

References 12 publications

Bivariate Bernstein–Schurer–Stancu type GBS operators in $(p,q)$-analogue

Bivariate Bernstein–Schurer–Stancu type GBS operators in $(p,q)$-analogue

Kantorovich variant of a new kind of q‐Bernstein–Schurer operators

Generalized Bernstein‐Kantorovich–type operators on a triangle

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