Some estimations of summation-integral-type operators

Mishra, Vishnu Narayan; Yadav, Rishikesh

doi:10.32513/tbilisi/1538532034

Cited by 10 publications

(10 citation statements)

References 30 publications

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“…Proof. One can prove the above all equalities with the help of equalities, which are proved in [19]. So we omit the proof.…”

Section: An Extension In the Sense Of Bivariate Operatorsmentioning

confidence: 97%

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Convergence of the summation-integral type operators via statistically

Yadav,

Meher,

Mishra

2019

Preprint

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Our main aim is to investigate the approximation properties for the summation integral type operators in statistical sense. In this regard, we prove the statistical convergence theorem using well known Korovkin theorem and the degree of approximation is determined. Also using weight function, the weighted statistical convergence theorem with the help of Korovkin theorem is obtained. The statistical rate of convergence in the terms of modulus of continuity and function belonging to the Lipschitz class are obtained. To support the convergence results of the proposed operators to the function, graphical representations take place and a comparison is shown with Szász-Mirakjan-Kantorovich operators through examples. The last section deals with, a bivariate extension of the proposed operators to study the rate of convergence for the function of two variables, additionally, convergence of the bivariate operators is shown with graphically.

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“…Proof. One can prove the above all equalities with the help of equalities, which are proved in [19]. So we omit the proof.…”

Section: An Extension In the Sense Of Bivariate Operatorsmentioning

confidence: 97%

“…So the main objective of this paper is to investigate the theory of approximation by considering the statistical convergence. Here the Korovkin theory is considered to deals with the approximation of function f by the operators { S * n,a (f ; x)} [19] for the summation integral type operators, which are as follows.…”

Section: Introductionmentioning

confidence: 99%

Convergence of the summation-integral type operators via statistically

Yadav,

Meher,

Mishra

2019

Preprint

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“…Many results related to approximations theory have also been discussed by many authors [5][6][7][8][9]. 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.…”

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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“…Also, another modification into Stancu variant appeared in [9] of the above operators (2) and related properties like density, direct results as well as Voronovskaya type theorem are studied. Many approximation results are also discussed in [14,20]. A natural generalization is carried out for the above operators (2) in [10] by Mishra et al for the study of simultaneous approximation, like…”

Section: Introductionmentioning

confidence: 99%

Further Approximations on Durrmeyer Modification of Szasz-Mirakjan Operators

Yadav

Meher

Mishra

2020

Eur. J. Pure Appl. Math.

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The main purpose of this paper is to determine the approximations of Durrmeyermodification of Szasz-Mirakjan operators, defined by Mishra et al. (Boll. Unione Mat. Ital. (2016) 8(4):297-305). We estimate the order of approximation of the operators for the functions belonging to the different spaces. Here, the rate of convergence of the said operators is established by means of the function with derivative of the bounded variation. At last, the graphical analysis is discussed to support the approximation results of the operators.

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Some estimations of summation-integral-type operators

Cited by 10 publications

References 30 publications

Convergence of the summation-integral type operators via statistically

Convergence of the summation-integral type operators via statistically

Approximation by associated GBS operators of Szász-Mirakjan type operators

Further Approximations on Durrmeyer Modification of Szasz-Mirakjan Operators

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