On Stancu type generalization of (p,q)-Baskakov-Kantorovich operators

Abstract

In the current paper, we introduce Stancu type generalization of Baskakov-Kantorovich operators based on (p; q)-integers and estimate the moments. We show the convergence of the new operators via the weighted Korovkin theorem. Then we investigate direct results by using Peetre's Kfunctional and modulus of continuity. In addition, we give pointwise estimation by the help of functions belonging to Lipschitz class. Moreover, we demonstrate the Voronovskaya-type theorem for the newly constructed operators. In the last section, we represent some illustrative graphics to show the convergence of the constructed operators to the selected function by using MATLAB.

A Modified Robotic Manipulator Controller Based on Bernstein-Kantorovich-Stancu Operator

“…As shown in Table 1 , compared with the classical BK operator [ 18 ], -BK [ 24 ] ( ), -BK [ 19 , 30 ] ( ), and -BK [ 31 ] ( ) make a comparison, and the error of the BKS operator proposed in this paper is smaller. Under the condition that of the model in this paper is satisfied, the error is the smallest.…”

“…They are mainly used to optimize the process of updating controller parameters to make it approach quickly and ensure accuracy [ 16 ]. Moreover, with the development of the BK operator, some improved BK operators, such as λ -BK [ 17 , 18 ], -BK [ 19 ], -BK [ 20 ], and other methods, have also been developed [ 21 , 22 , 23 , 24 ]. In this paper, a new BKS operator, which is introduced in [ 25 ], is implemented in the manipulator controller to optimize the parameter update process of the disturbance observer and improve the trajectory tracking accuracy of the robotic manipulator controller.…”

Results on Bivariate Modified (p, q)-Bernstein Type Operators

“…Firstly, Mursaleen et al carried this concept to the approximation theory [7]. After then, (𝑝, 𝑞)operators have been studied by different authors for examples [8][9][10][11][12][13][14][15][16][17]. Karaisa [18] defined bivariate form of (𝑝, 𝑞)-Bernstein operators.…”

On some Statistical Approximation Properties of Generalized Lupas-Stancu Operators

“…converge to continuous function f (u) uniformly in [0, 1] for each real γ, δ such that 0 ≤ γ ≤ δ. For more recent literatures on Stancu type operators on can see [1,4,7,[15][16][17][23][24][25][26][27][28][29][30][31].…”