Approximation results of Phillips type operators including exponential function
Prerna Sharma, Diwaker Sharma
Article ID: 2821
Vol 2, Issue 2, 2024
DOI:
https://doi.org/10.54517/mss.v2i2.2821
Received: 9 July 2024; Accepted: 24 September 2024; Available online: 6 October 2024; Issue release: 15 November 2024
Download PDF
Abstract
The current article deals with a study on some moderation of the Phillips operators, including constant and exponential functions. Here, we derive the moments applying the notion of moment-generating function for the well-known Phillips operators. The authors also establish uniform convergence estimates for the improved form of these operators. Additionally, some direct estimates involving the asymptotic-type results are discussed.
Keywords
Phillips operators; approximation; exponential functions; moments; linear positive operators
References
Baskakov VA. An example of sequence of linear positive operators in the space of continuous functions. SSSR. 1957; 113: 249–251.
Abel U, Gupta V, Sisodia M. Some new semi-exponential operators. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales Serie A Matemáticas. 2022; 116(2). doi: 10.1007/s13398-022-01228-2
Abel U, Gupta V. The rate of convergence of a generalization of Post–Widder operators and Rathore operators. Advances in Operator Theory. 2023; 8(3). doi: 10.1007/s43036-023-00272-y
Gupta V, Anjali A. A new type of exponential operator. Filomat. 2023; 37(14): 4629-4638. doi: 10.2298/fil2314629g
Gupta V. Higher order Lupaş-Kantorovich operators and finite differences. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales Serie A Matemáticas. 2021; 115(3). doi: 10.1007/s13398-021-01034-2
Sharma P, Sharma D. Some Statistical Approximation based on post-Widder operators. JOURNAL OF ADVANCES IN MATHEMATICS. 2023; 22: 23-29. doi: 10.24297/jam.v22i.9451
Sharma P. Study of some approximation estimates concerning convergence of (p, q)-variant of linear positive operators. In: Proceedings of the International E-Conference on Mathematical and Statistical Sciences A Selçuk Meeting. 2022; pp. 166-174.
Sharma P. Approximation by Some Stancu Type Linear Positive Operators. Journal of Nepal Mathematical Society. 2022; 5(2): 34-41. doi: 10.3126/jnms.v5i2.50017
Phillips RS. An Inversion Formula for Laplace Transforms and Semi-Groups of Linear Operators. The Annals of Mathematics. 1954; 59(2): 325. doi: 10.2307/1969697
Ditzian Z. On Global Inverse Theorems of Szász and Baskakov Operators. Canadian Journal of Mathematics. 1979; 31(2): 255-263. doi: 10.4153/cjm-1979-027-2
Finta Z, Gupta V. Direct and inverse estimates for Phillips type operators. Journal of Mathematical Analysis and Applications. 2005; 303(2): 627-642. doi: 10.1016/j.jmaa.2004.08.064
Kiliçman A, Ayman-Mursaleen M, Nasiruzzaman Md. A note on the convergence of Phillips operators by the sequence of functions via q-calculus. Demonstratio Mathematica. 2022; 55(1): 615-633. doi: 10.1515/dema-2022-0154
May CP. On Phillips operators. Journal Approx. Theory. 1997; 20: 315-322.
Mursaleen M, Nasiruzzaman M, Kilicman A, et al. Dunkl Generalization of Phillips Operators and Approximation in Weighted Spaces. Adv. Diff. Equ. 2020; 365.
Sharma PM. Approximation Properties of Certain q-Genuine Szász Operators. Complex Analysis and Operator Theory. 2016; 12(1): 27-36. doi: 10.1007/s11785-016-0538-3
Tachev G. A Global Inverse Theorem for Combinations of Phillips Operators. Mediterranean Journal of Mathematics. 2015; 13(5): 2709-2719. doi: 10.1007/s00009-015-0648-6
King JP. Positive linear operators which preserve x2. Acta Math. Hungar. 2003; 99(3): 203–208.
Gupta V. A note on modified Phillips operators. Southeast Asian Bull. Math. 2010; 34: 847–851.
Acar T, Aral A, Gonska H. On Szasz-Mirakyan operators preserving e2ax, a>0. Mediterr. Journal Math. 2017; 14(6): 1–14.
Boyanov BD, Veselinov VM. A note on the approximation of functions in an infinite interval by linear positive operators. Bull. Math. Soc. Sci. Math. Roum. 1970; 14(62): 9–13.
Holhos A. The rate of approximation of functions in an infinite interval by positive linear operators. Stud. Univ. Babes-Bolyai Math. 2010; (2): 133–142.
Heilmann M, Tachev G. Commutatively, direct and strong converse results for Phillips operators. East Jouanl Approx. 2011; 17(3): 299–317.
Refbacks
- There are currently no refbacks.
Copyright (c) 2024 Prerna Sharma, Diwaker Sharma
License URL:
https://creativecommons.org/licenses/by/4.0/