Better Approximation of Functions by Genuine Baskakov Durrmeyer Operators

Abstract

In this paper, we define a new genuine Baskakov-Durrmeyer operators. We give uniform convergence using the weighted modulus of continuity. Then we study direct approximation of the operators in terms of the moduli of smoothness. After that a Voronovskaya type result is studied.

Keywords

• Genuine Baskakov Durrmeyer operators,weighted modulus of continuity,Voronovskaya theorem

References

1. D. Cardenas-Morales, P. Garrancho, I. Raşa, Bernstein-type Operators which Preserve Polynomials , Computers and Mathematics with Applications 62 (2011) 158-163.
2. T. Acar, A. Aral, I. Raşa, Modied Bernstein-Durrmeyer Operators, General Mathematics 22(1) (2014) 27-41.
3. T. Acar, A. Aral, I. Rasa, Positive Linear Operators Preserving  and  2, Constructive Mathe- matical Analysis 2(3) (2019) 98-102.
4. T. Acar, G. Ulusoy, Approximation by Modied Szasz Durrmeyer Operators, Periodica Mathe- matica Hungarica 72 (2016) 64-75.
5. T. Acar, V. Gupta, A. Aral, Rate of Convergence for Generalized Szasz Operators, Bulletin of Mathematical Science 1(1) (2011) 99-113.
6. A. Aral, D. Inoan, I. Raşa, On the Generalized Szasz-Mirakyan Operators, Results in Mathematics 65 (2014) 441-452.
7. M. Bodur, O. G. Yilmaz, A. Aral, Approximation by Baskakov-Szasz-Stancu Operators Preserving Exponential Functions, Constructive Mathematical Analysis 1(1) (2018) 1-8.
8. Z. Finta, A Quantitative Variant of Voronovskaja's Theorem for King-Type Operators, Construc- tive Mathematical Analysis 2(3) (2019) 124-129.

9. R. Maurya, H. Sharma, C. Gupta, Approximation Properties of Kantorovich Type Modications of (p, q)-Meyer-Konig-Zeller Operators, Constructive Mathematical Analysis 1(1) (2018) 58-72.
10. G. Ulusoy Ada, On the Generalized Baskakov Durrmeyer Operators, Sakarya University Journal of Science 23(4) (2019) 549-553.
11. Z. Finta, On Converse Approximation Theorems, Journal of Mathematical Analysis and Appli- cations 312(1) (2005) 159-180.
12. A. Holhos, Quantitative Estimates for Positive Linear Operators in Weighted Space, General Mathematics 16(4) (2008) 99-110.
13. A. Ciupa, A Class of Integral Favard Szasz Type Operators, Studia Universitatis Babes-Bolyai Mathematica 40(1) (1995) 39-47.
14. A. D. Gadziev, The Convergence Problem for a Sequence of Positive Linear Operators on Unbounded Sets and Theorems Analogues to that of P. P. Korovkin, Doklady Akademii Nauk SSSR 218 (1974) 1001-1004, Also in Soviet Mathematics Doklady 15 (1974) 1433-1436.