Year 2016,
Volume: 65 Issue: 1, 187 - 195, 01.02.2016
Abstract
In this paper, we consider power series method which is also member of the class of all continuous summability methods. We study a Korovkintype approximation theorem for the Mastroianni operators with the use ofpower series method which includes Abel and Borel methods. We also givesome estimates in terms of the modulus of continuity and the second modulusof smoothness
Keywords
Power series method Korovkin type approximation theorem Mastroianni operators quantitative estimates
References
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- O. G. Atlihan and C. Orhan, Matrix summability and positive linear operators, Positivity 11 (2007), 387-398.
- J. Boos, Classical and Modern Methods in Summability, Oxford University Press (2000).
- P. L. Butzer and H. Berens, Semi-groups of operators and approximation, Die Grundlehren der Mathematischen Wissenschaften, 145, Springer, New York, (1967).
- O. Duman, M. K. Khan and C. Orhan, A statistical convergence of approximating operators, Math. Inequal. Appl. 6 (2003), 689-699.
- O. Duman, Summability process by Mastroianni operators and their generalizations, Mediterr. J. Math. 12 (2015), 21-35.
- A. Holhos, Uniform approximation of functions by Bernstein-Stancu operators, Carpathian J. Math. 31 (2015), 205-212.
- A. D. Gadjiev and C. Orhan, Some approximation theorems via statistical convergence, Rocky Mountain J. Math. 32 (2002), 129-138.
- P. P. Korovkin, Linear Operators and Approximation Theory, Hindustan Publ. Co., Delhi, (1960).
- W. Kratz and U. Stadtmüller, Tauberian theorems for Jp-summability, J. Math. Anal. Appl. (1989), 362-371.
- G. Mastroianni, On a linear positive operator, Rend. Acad. Sci. Fis. Mat. Napoli 46 (1979), 176.
- A. J. López-Moreno and J. M. Latorre-Palacios, Localization results for generalized Baskakov/Mastroianni and composite operators, J. Math. Anal. Appl. 380 (2011), 425-439.
- A. J. López-Moreno, J. Martínez-Moreno and F. Muñ oz-Delgado and J. M. Quesada, Some properties of linear positive operators de…ned in terms of …nite diğerences. Multivariate approximation and interpolation with applications (Almuñécar, 2001) 87-96, Monogr. Real
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- U. Stadtmüller and A. Tali, On certain families of generalized Nörlund methods and power series methods, J. Math. Anal. Appl. 238 (1999), 44-66.
Year 2016,
Volume: 65 Issue: 1, 187 - 195, 01.02.2016
Abstract
References
- O. Agratini and B. Della Vecchia, Mastroianni operators revisited, Facta Univ. Ser. Math. Inform 19 (2004), 53-63.
- F. Altomare and M. Campiti, Korovkin-type approximation theory and its applications, De Gruyter Studies in Mathematics, 17, Walter de Gruyter Co., Berlin (1994).
- F. Altomare, Korovkin-type theorems and approximation by positive linear operators, Surv. Approx. Theory, 5 (2010), 92-164.
- O. G. Atlihan and C. Orhan, Matrix summability and positive linear operators, Positivity 11 (2007), 387-398.
- J. Boos, Classical and Modern Methods in Summability, Oxford University Press (2000).
- P. L. Butzer and H. Berens, Semi-groups of operators and approximation, Die Grundlehren der Mathematischen Wissenschaften, 145, Springer, New York, (1967).
- O. Duman, M. K. Khan and C. Orhan, A statistical convergence of approximating operators, Math. Inequal. Appl. 6 (2003), 689-699.
- O. Duman, Summability process by Mastroianni operators and their generalizations, Mediterr. J. Math. 12 (2015), 21-35.
- A. Holhos, Uniform approximation of functions by Bernstein-Stancu operators, Carpathian J. Math. 31 (2015), 205-212.
- A. D. Gadjiev and C. Orhan, Some approximation theorems via statistical convergence, Rocky Mountain J. Math. 32 (2002), 129-138.
- P. P. Korovkin, Linear Operators and Approximation Theory, Hindustan Publ. Co., Delhi, (1960).
- W. Kratz and U. Stadtmüller, Tauberian theorems for Jp-summability, J. Math. Anal. Appl. (1989), 362-371.
- G. Mastroianni, On a linear positive operator, Rend. Acad. Sci. Fis. Mat. Napoli 46 (1979), 176.
- A. J. López-Moreno and J. M. Latorre-Palacios, Localization results for generalized Baskakov/Mastroianni and composite operators, J. Math. Anal. Appl. 380 (2011), 425-439.
- A. J. López-Moreno, J. Martínez-Moreno and F. Muñ oz-Delgado and J. M. Quesada, Some properties of linear positive operators de…ned in terms of …nite diğerences. Multivariate approximation and interpolation with applications (Almuñécar, 2001) 87-96, Monogr. Real
- Acad. Ci. Exact. Fís.-Quím. Nat. Zaragoza, 20, Acad. Cienc. Exact. Fís. Quím. Nat. Zaragoza, Zaragoza (2002).
- U. Stadtmüller and A. Tali, On certain families of generalized Nörlund methods and power series methods, J. Math. Anal. Appl. 238 (1999), 44-66.
There are 17 citations in total.
Details
| Primary Language | English |
|---|---|
| Journal Section | Research Articles |
| Authors | |
| Publication Date | February 1, 2016 |
| Published in Issue | Year 2016 Volume: 65 Issue: 1 |
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Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.
