Approximation by ( p , q ) $(p,q)$ -Lupaş–Schurer–Kantorovich operators

Abstract

In the current paper, we examine the -analogue of Kantorovich type Lupaş–Schurer operators with the help of -Jackson integral. Then, we estimate the rate of convergence for the constructed operators by using the modulus of continuity in terms of a Lipschitz class function and by means of Peetre’s K-functionals based on Korovkin theorem. Moreover, we illustrate the approximation of the -Lupaş–Schurer–Kantorovich operators to appointed functions by the help of Matlab algorithm and then show the comparison of the convergence of these operators with Lupaş–Schurer operators based on -integers.

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.…”

Adaptation of the Kantorovich Type Integral to the Dunkl Operator

“…The famous people in the approximation theory are defined the well-known operators and given the most important theorems as Bernstein, 1912;Szász, 1950;Korovkin, 1953;Lorentz, 1953;Gadzhiev, 1974;Altomare & Campiti, 1994;Jakimovski & Leviatan, 1969;DeVore & Lorentz, 1993. ln the recent years, many results about the generalization of the operators including Gamma function have been obtained by mathematicians (İçöz & Çekim, 2016;Sucu et al, 2012;Mursaleen et al, 2016;Kanat & Sofyalıoğlu, 2018;2019;Nasiruzzaman & Aljohani, 2020a, 2020bYazici et al, 2022). Sucu (2014) gave the Dunkl-analogue of Szász-Mirakyan operator as follows…”

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

“…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.…”