Approximation properties of bivariate extension of q-Szász-Mirakjan-Kantorovich operators

Örkçü, Mediha

doi:10.1186/1029-242x-2013-324

Cited by 10 publications

(7 citation statements)

References 17 publications

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“…The Durrmeyer type modification of Bernstein operators, Baskakov operators and Szász-Mirakyan operators are studied in [23][24][25][26][27][28][29]. Motivated by such type of operators, we generalize the operators L…”

Section: Extensionsmentioning

confidence: 99%

On new class of linear and positive operators

Patel

Mishra

2015

Boll Unione Mat Ital

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Section: Extensionsmentioning

confidence: 99%

On new class of linear and positive operators

Patel

Mishra

2015

Boll Unione Mat Ital

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“…Despite these, if we move towards the operators defined over an infinite interval, then we look at the Szász-Mirakjan operators, which were introduced and studied by Mirakjan and Szász [10,11] independently and so many work done in a bivariate direction of these operators to generalize and check the behavior of the operators for the function of two variables. Later on Szász-Mirakjan operators have been discussed theoretically, numerically as well graphically by many authors [12][13][14][15] using bivariate extension for approximation of the functions of two variables.…”

Section: Introductionmentioning

confidence: 99%

Approximation by associated GBS operators of Szász-Mirakjan type operators

Yadav

Meher

Mishra

2021

Filomat

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In this article, the approximation properties of bivariate Sz?sz-Mirakjan type operators are studied for the function of two variables and rate of convergence of the bivariate operators is determined in terms of total and partial modulus of continuity. An associated GBS (Generalized Boolean Sum)-form of the bivariate Sz?sz-Mirakjan type operators is considered for the function of two variables to find an approximation of B-continuous and B-differentiable function in the B?gel?s space. Further, the degree of approximation of the GBS type operators is found in terms of mixed modulus of smoothness and functions belonging to the Lipschitz class as well as a pioneering result is obtained in terms of Peetre K-functional. Finally, the rate of convergence of the bivariate Sz?sz-Mirakjan type operators and the associated GBS type operators are examined through graphical representation for the finite and infinite sum which shows that the rate of convergence of the associated GBS type operators is better than the bivariate Sz?sz-Mirakjan type operators and also a comparison is taken place for the bivariate operators with bivariate Kantorovich operators.

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“…The concept of statistical convergence has been de…ned by Fast [2] and studied by many other authors. It is well known that every ordinary convergent sequence is statistically convergent but the converse is not true, examples and some related work can be found in [3,4,5,6,7]. The idea -statistical convergence was introduced by Akt¼ uglu in [8] as follows: Let (n) and (n) be two sequences positive numbers which satisfy the following conditions The concept of weighted -statistically convergence was developed by Karakaya and Karaisa [9].…”

Section: Introductionmentioning

confidence: 99%

“…The concept of statistical convergence has been defined by Fast [2] and studied by many other authors. It is well know that every statistically convergent sequence is ordinary convergent, but the converse is not true, examples and some related work can be found in [3][4][5][6][7][8]. The idea αβ-statistical convergence was introduced by Aktȗglu in [9] as follows:…”

Section: Introductionmentioning

confidence: 99%