Blending Type Approximation by GBS Operators of Generalized Bernstein–Durrmeyer Type

Kajla, Arun; Miclăuş, Dan

doi:10.1007/s00025-018-0773-1

Cited by 54 publications

(26 citation statements)

References 17 publications

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“…Let

f \in R^{X} = false{f : X \to double-struckR false}

. The GBS operator associated to a linear operator

P : R^{X} \to R^{X}

is defined as

\begin{matrix} G false(f; x, y false) & = G false[f false(u, v false); x, y false] \\ = P false[f false(u, y false) + f false(x, v false) - f false(u, v false); x, y false] . \end{matrix}

During time some researchers constructed and studied different type of GBS operators as we can see for example papers in Bărbosu et al, Kajla and Miclăuş, and Ruchi et al…”

Section: Approximation By Associated Gbs Operatorsmentioning

confidence: 99%

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Some approximation properties by a class of bivariate operators

Acu

Acar

Muraru

et al. 2019

Math Methods in App Sciences

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Starting with the well‐ known Bernstein operators, in the present paper, we give a new generalization of the bivariate type. The approximation properties of this new class of bivariate operators are studied. Also, the extension of the proposed operators, namely, the generalized Boolean sum (GBS) in the Bögel space of continuous functions is given. In order to underline the fact that in this particular case, GBS operator has better order of convergence than the original ones, some numerical examples are provided with the aid of Maple soft. Also, the error of approximation for the modified Bernstein operators and its GBS‐type operator are compared.

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“…Let

f \in R^{X} = false{f : X \to double-struckR false}

. The GBS operator associated to a linear operator

P : R^{X} \to R^{X}

is defined as

\begin{matrix} G false(f; x, y false) & = G false[f false(u, v false); x, y false] \\ = P false[f false(u, y false) + f false(x, v false) - f false(u, v false); x, y false] . \end{matrix}

During time some researchers constructed and studied different type of GBS operators as we can see for example papers in Bărbosu et al, Kajla and Miclăuş, and Ruchi et al…”

Section: Approximation By Associated Gbs Operatorsmentioning

confidence: 99%

“…exists and is finite. During time some researchers constructed and studied different type of GBS operators as we can see for example papers in Bȃrbosu et al, 18 Kajla and Miclȃuş, 19 and Ruchi et al 20 Let f ∈ C b (I 2 ). The GBS operator G M n,m associated to B M n,m can be introduced as follows…”

Section: Approximation By Associated Gbs Operatorsmentioning

confidence: 99%

Some approximation properties by a class of bivariate operators

Acu

Acar

Muraru

et al. 2019

Math Methods in App Sciences

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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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“…For the special case, = 1; these operators reduce the well-known Bernstein operators. In [19], Kajla and Acar introduced a sequence of summation-integral type operators as follows:…”

Section: Introductionmentioning

confidence: 99%

“…In [19], Voronoskaja type asymptotic formula, rate of convergence, local and global convergence results were established for these operators (1.2).…”

Section: Introductionmentioning

confidence: 99%

Blending type approximation by bézier-summation-integral type operators

Acar¹,

Kajla²

2018

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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Abstract. In this note we construct the Bézier variant of summation integral type operators based on a non-negative real parameter. We present a direct approximation theorem by means of the …rst order modulus of smoothness and the rate of convergence for absolutely continuous functions having a derivative equivalent to a function of bounded variation. In the last section, we study the quantitative Voronovskaja type theorem.

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Blending Type Approximation by GBS Operators of Generalized Bernstein–Durrmeyer Type

Cited by 54 publications

References 17 publications

Some approximation properties by a class of bivariate operators

Some approximation properties by a class of bivariate operators

Generalized Bernstein‐Kantorovich–type operators on a triangle

Blending type approximation by bézier-summation-integral type operators

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