Approximation by bivariate (<i>p</i>,<i>q</i>)-Baskakov–Kantorovich operators

İlarslan, Hatice Gül İnce; Acar, Tuncer

doi:10.1515/gmj-2016-0057

Cited by 33 publications

(13 citation statements)

References 11 publications

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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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Section: Introductionmentioning

confidence: 99%

Generalized Bernstein‐Kantorovich–type operators on a triangle

Kajla

2019

Math Methods in App Sciences

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“…They have also investigated several approximation properties by defining different positive linear operators in an approximation process based on a -analogue (see [1–8, 14, 18, 23–25]). Recently they have also studied the Szász-type operators via Dunkl generalizations (see [17, 20–22, 28]).…”

Section: Introductionmentioning

confidence: 99%

A Dunkl type generalization of Szász operators via post-quantum calculus

2018

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The object of this paper to construct Dunkl type Szász operators via post-quantum calculus. We obtain some approximation results for these new operators and compute convergence of the operators by using the modulus of continuity. Furthermore, we obtain the rate of convergence of these operators for functions belonging to the Lipschitz class. We also study the bivariate version of these operators.

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“…They investigated the approximation properties of above mentioned operators using the techniques of (p; q)-calculus. Also we can refer the readers to some recent papers: (p; q)-Baskakov-Kantorovich operators [3], bivariate (p; q)-Bernstein Kantorovich operators [4], bivariate (p; q)-BaskakovKantorovich operators [12].…”

Section: Introductionmentioning

confidence: 99%