Bivariate α,q-Bernstein–Kantorovich Operators and GBS Operators of Bivariate α,q-Bernstein–Kantorovich Type

Cai, Qing-Bo; Cheng, Wen-Tao; Çekіm, Bayram

doi:10.3390/math7121161

Cited by 4 publications

(2 citation statements)

References 20 publications

(19 reference statements)

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“…Subsequently, Cai et al establish a more general approach to Kantorovich operators known as bivariate α, q-Bernstein-Kantorovich operators in (Cai et al 2019) as:…”

Section: Literature Reviewmentioning

confidence: 99%

Different Variants of Bernstein Kantorovich Operators and Their Applications in Sciences and Engineering Field

BAWA,

BHARDWAJ,

BHATİA

2023

Chaos Theory and Applications

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In this article, we investigate various Bernstein-Kantorovich variants together with their approximation properties. Nowadays, these variants of Bernstein-Kantorovich operators have been a source of inspiration for researchers as it helps to approximate integral functions also which is not feasible in the case of discrete operators. Chaos theory has also been referred to as complexity theory. Using chaos theory complexity is also reduced as in approximation theory. Thus in order to reduce complexity and to have better understanding of images in sciences and engineering field, sampling Kantorovich operators of approximation theory are widely used in this regard for enhancement of images. Thus, we discuss the important applications of Kantorovich operators depicting pragmatic and theoretical aspects of approximation theory.

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“…Subsequently, Cai et al establish a more general approach to Kantorovich operators known as bivariate α, q-Bernstein-Kantorovich operators in (Cai et al 2019) as:…”

Section: Literature Reviewmentioning

confidence: 99%

Different Variants of Bernstein Kantorovich Operators and Their Applications in Sciences and Engineering Field

BAWA,

BHARDWAJ,

BHATİA

2023

Chaos Theory and Applications

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show abstract

“…Moreover, let set of all ordinary continuous function defined on M 1 × M 2 be C(M 1 × M 2 ) . For further details on space of Bögel functions and GBS-type operators related to this paper, we propose the article [33][34][35][36][37][38].…”

Section: Gbs-type Approximation In Bögel Spacementioning

confidence: 99%

Approximation of GBS Type q-Jakimovski-Leviatan-Beta Integral Operators in Bögel Space

Alotaibi

2022

Mathematics

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In the present article, we introduce the bivariate variant of Beta integral type operators based on Appell polynomials via q-calculus. We study the local and global type approximation properties for these new operators. Next, we introduce the GBS form for these new operators and then study the degree of approximation by means of modulus of smoothness, mixed modulus of smoothness and Lipschitz class of Bögel continuous functions.

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Approximation of functions by a class of Durrmeyer–Stancu type operators which includes Euler’s beta function

et al. 2021

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In this work, we construct the genuine Durrmeyer–Stancu type operators depending on parameter α in $[0,1]$ [ 0 , 1 ] as well as $\rho >0$ ρ > 0 and study some useful basic properties of the operators. We also obtain Grüss–Voronovskaja and quantitative Voronovskaja types approximation theorems for the aforesaid operators. Further, we present numerical and geometrical approaches to illustrate the significance of our new operators.

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Bivariate α,q-Bernstein–Kantorovich Operators and GBS Operators of Bivariate α,q-Bernstein–Kantorovich Type

Cited by 4 publications

References 20 publications

Different Variants of Bernstein Kantorovich Operators and Their Applications in Sciences and Engineering Field

Different Variants of Bernstein Kantorovich Operators and Their Applications in Sciences and Engineering Field

Approximation of GBS Type q-Jakimovski-Leviatan-Beta Integral Operators in Bögel Space

Approximation of functions by a class of Durrmeyer–Stancu type operators which includes Euler’s beta function

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