Approximation on a class of Sz\xe1sz\u2013Mirakyan operators via second kind of beta operators

M Nasiruzzaman,Ravi Kumar,Nadeem Rao,Anshul Srivastava

doi:10.1186/s13660-020-02317-9

Abstract

In the present article, we construct a new sequence of positive linear operators via Dunkl analogue of modified Szász–Durrmeyer operators. We study the moments and basic results. Further, we investigate the pointwise approximation and uniform approximation results in various functional spaces for these sequences of positive linear operators. Finally, we prove the global approximation and A-statistical convergence results for these operators.

Highlights

1 Introduction In recent past, the Szász–Mirakjan operators and Szász–Durrmeyer type operators have been intensively investigated in various functional spaces to approximate the continuous functions and Lebesgue measurable functions respectively
We have defined the Szász–Mirakyan integral operators based on Dunkl analogue with the aid of two nonnegative parameters 0 ≤ α ≤ β
This type of modification enables us to give a generalied error estimation for a certain function in comparison to the Szász–Mirakyan integral operators based on Dunkl analogue

Summary

Introduction

The Szász–Mirakjan operators and Szász–Durrmeyer type operators have been intensively investigated in various functional spaces to approximate the continuous functions and Lebesgue measurable functions respectively. }. Researchers have obtained several approximations of Szász–Mirakyan type operators via Dunkl generalization; for instance, see [6, 18, 26, 28, 29, 32, 39]. Related to these results, more approximation results have been studied in different functional spaces (see [1, 2, 4, 5, 14, 38] and [3, 16, 27, 31]). Global approximation results are studied in [19,20,21, 24, 25, 35]

Preliminary results

Conclusion

Methods