A Generalization of Szasz Operators by Using the Appell Polynomials of Class A(2)
Abstract
:1. Introduction
2. Convergence of the Operators and Some Approximation Results
3. Numerical Example
4. Concluding Remarks
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
- Szasz, O. Generalization of S. Bernstein’s polynomials to the infinite interval. J. Res. Nat. Bur. Stand. 1950, 45, 239–245. [Google Scholar] [CrossRef]
- Jakimovski, A.; Leviatan, D. Generalized Szasz operators for the approximation in the infinite interval. Mathematica 1969, 11, 97–103. [Google Scholar]
- Ismail, M.E.H. On a generalization of Szász operators. Mathematica 1974, 39, 259–267. [Google Scholar]
- Aktaş, R.; Çekim, B.; Taşdelen, F. A Dunkl analogue of operators including two-variable Hermite polynomials. Bull. Malaysian Math. Sci. Soc. 2019, 42, 2795–2805. [Google Scholar] [CrossRef] [Green Version]
- Cai, Q.B.; Çekim, B.; İçöz, G. Gamma generalization operators involving analytic functions. Mathematics 2021, 9, 1547. [Google Scholar] [CrossRef]
- Çekim, B.; Aktaş, R.; Taşdelen, F. A Dunkl-Gamma type operator in terms of generalization of two-variable Hermite polynomials. Indian J. Pure Appl. Math. 2021, 1–9. [Google Scholar] [CrossRef]
- İçöz, G.; Varma, S.; Sucu, S. Approximation by operators including generalized Appell polynomials. Filomat 2016, 30, 429–440. [Google Scholar] [CrossRef]
- Gupta, P.; Acu, A.M.; Agrawal, P.N. Jakimovski–Leviatan operators of Kantorovich type involving multiple Appell polynomials. Georgian Math. J. 2021, 28, 73–82. [Google Scholar] [CrossRef]
- Mursaleen, M.; Rahman, S.; Ansari, K.J. Approximation by Jakimovski-Leviatan-Stancu-Durrmeyer type operators. Filomat 2019, 33, 1517–1530. [Google Scholar] [CrossRef] [Green Version]
- Srivastava, H.M.; Içöz, G.; Çekim, B. Approximation properties of an extended family of the Szász–Mirakjan beta-type operators. Axioms 2019, 8, 111. [Google Scholar] [CrossRef] [Green Version]
- Sucu, S.; İçöz, G.; Varma, S. On some extensions of Szasz operators including Boas-Buck-type polynomials. Abstr. Appl. Anal. 2012, 15, 680340. [Google Scholar] [CrossRef] [Green Version]
- Varma, S.; Sucu, S.; İçöz, G. Generalization of Szasz operators involving Brenke type polynomials. Comput. Math. Appl. 2012, 64, 121–127. [Google Scholar] [CrossRef] [Green Version]
- Kazmin, Y.A. On Appell polynomials. Mat. Zametki 1969, 6, 161–172, English translation in Math. Notes 1969, 5, 556–562. [Google Scholar] [CrossRef]
- Altomare, F.; Campiti, M. Korovkin-type approximation theory and its applications. In Appendix A by Michael Pannenberg and Appendix B by Ferdinand Beckhoff, de Gruyter Studies in Mathematics; Walter de Gruyter & Co.: Berlin, Germany, 1994. [Google Scholar]
- Devore, R.A.; Lorentz, G.G. Constructive Approximation; Springer: Berlin/Heidelberg, Germany, 1993. [Google Scholar]
- Gavrea, I.; Rasa, I. Remarks on some quantitative Korovkin-type results. Rev. Anal. Numér. Théor. Approx. 1993, 22, 173–176. [Google Scholar]
- Zhuk, V.V. Functions of the Lip1 class and S. N. Bernstein’s polynomials (Russian), Vestnik Leningrad. Univ. Mat. Mekh. Astronom. 1989, 1, 25–30. [Google Scholar]
- Gould, H.W.; Hopper, A.T. Operational formulas connected with two generalizations of Hermite polynomials. Duke Math. J. 1962, 29, 51–63. [Google Scholar] [CrossRef]
- Douak, K. The relation of the d-orthogonal polynomials to the Appell polynomials. J. Comput. Appl. Math. 1996, 70, 279–295. [Google Scholar] [CrossRef] [Green Version]
- Iseghem, J.V. Vector orthogonal relations. Vector QD-algorithm. J. Comput. Appl. Math. 1987, 19, 141–150. [Google Scholar] [CrossRef] [Green Version]
- Maroni, P. L’orthogonalitè et les recurrences de polynômes d’ordre superieur à deux. Ann. Fac. Sci. Toulouse Math. 1989, 10, 105–139. [Google Scholar] [CrossRef]
n | Estimation for | Estimation for | Estimation for |
---|---|---|---|
10 | 0.6423250428 | 1.1805569940 | 1.4096205150 |
0.2100772120 | 0.2409468484 | 0.2812002468 | |
0.0668966700 | 0.0679554484 | 0.0695336528 | |
0.0211952592 | 0.0212291148 | 0.0212804728 | |
0.0067064284 | 0.0067075012 | 0.0067091310 | |
0.0021211432 | 0.0021211772 | 0.0021212294 | |
0.0006708028 | 0.0006708042 | 0.0006708056 |
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |
© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
Varma, S.; Sucu, S. A Generalization of Szasz Operators by Using the Appell Polynomials of Class A(2). Symmetry 2022, 14, 1410. https://doi.org/10.3390/sym14071410
Varma S, Sucu S. A Generalization of Szasz Operators by Using the Appell Polynomials of Class A(2). Symmetry. 2022; 14(7):1410. https://doi.org/10.3390/sym14071410
Chicago/Turabian StyleVarma, Serhan, and Sezgin Sucu. 2022. "A Generalization of Szasz Operators by Using the Appell Polynomials of Class A(2)" Symmetry 14, no. 7: 1410. https://doi.org/10.3390/sym14071410
APA StyleVarma, S., & Sucu, S. (2022). A Generalization of Szasz Operators by Using the Appell Polynomials of Class A(2). Symmetry, 14(7), 1410. https://doi.org/10.3390/sym14071410