Warianty tytułu
Języki publikacji
Abstrakty
The basic aim of this study is to include nonnegative real parameters to allow for approximation findings of the Stancu variant of Phillips operators. We concentrate on the uniform modulus of smoothness in a simple manner before moving on to the approximation in weighted Korovkin’s space. Our study’s goals and outcomes are to fully develop the uniformly approximated findings of Phillips operators. We determine the order of convergence in terms of Lipschitz maximal function and Peetre’s K-functional. In addition, the Voronovskaja-type theorem is also proved.
Czasopismo
Rocznik
Tom
Strony
615--633
Opis fizyczny
Bibliogr. 39 poz.
Twórcy
autor
- Department of Mathematics and Statistics, Faculty of Science, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia, akilic@upm.edu.my
- Department of Mathematics and Statistics, Faculty of Science, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia, mohammad.mursaleen@uon.edu.au
- School of Information and Physical Sciences, The University of Newcastle, University Drive, Callaghan, New South Wales 2308, Australia
autor
- Computational and Analytical Mathematics and Their Applications Research Group, Department of Mathematics, Faculty of Science, University of Tabuk, PO Box 4279, Tabuk 71491, Saudi Arabia, nasir3489@gmail.com
Bibliografia
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- [3] S. Sucu, Dunkl analogue of Szász operators, Appl. Math. Comput. 244 (2014), 42–48, DOI: https://doi.org/10.1016/j.amc.2014.06.088.
- [4] G. İçöz and B. Çekim, Dunkl generalization of Szász operators via q-calculus, J. Ineq. Appl. 2015 (2015), 284, DOI: https://doi.org/10.1186/s13660-015-0809-y.
- [5] B. Cheikh, Y. Gaied, and M. Zaghouani, A q-Dunkl-classical q-Hermite type polynomials, Georgian Math. J. 21 (2014), 125–137, DOI: https://doi.org/10.1515/gmj-2014-0022.
- [6] F. H. Jackson, On q-definite integrals, Quart. J. Pure Appl. Math. 15 (1910), 193–203.
- [7] C. P. May, On Phillips operators, J. Approx. Theory 20 (1977), 315–322, DOI: https://doi.org/10.1016/0021-9045(77)90078-8.
- [8] M. Mursaleen, S. Tabassum, and R. Fatma, On q-statistical summability method and its properties, Iranian J. Sci. Tech. Trans. A: Sci. 46 (2022), no. 2, 455–460, DOI: https://doi.org/10.1007/s40995-022-01285-7.
- [9] M. Ayman-Mursaleen and S. Serra-Capizzano, Statistical convergence via q -calculus and a Korovkin’s type approximation theorem, Axioms 11 (2022), 70, DOI: https://doi.org/10.3390/axioms11020070.
- [10] T. Khan, S. A. Khan, and N. Rao, On approximation by bivariate Szász-Gamma type hybrid operators, J. Math. Anal. Appl. 14 (2022), 11–27, DOI: https://doi.org/10.54671/bmaa-2022-1-2.
- [11] A. Kiliçman, M. Ayman-Mursaleen, and A. A. H. A. Al-Abied, Stancu type Baskakov-ŤDurrmeyer operators and approximation properties, Mathematics 8 (2020), 1164, DOI: https://doi.org/10.3390/math8071164.
- [12] T. Acar, Quantitative q-Voronovskaya and q-Grüss-Voronovskaya-type results for q-Szász operators, Georgian Math. J. 23 (2016), 459–468, DOI: https://doi.org/10.1515/gmj-2016-0007.
- [13] A. Alotaibi, M. Nasiruzzaman, and M. Mursaleen, A Dunkl type generalization of Szász operators via post-quantum calculus, J. Inequal. Appl. 2018 (2018), 287, DOI: https://doi.org/10.1186/s13660-018-1878-5.
- [14] R. Aslan, On a Stancu form Szász-Mirakjan-Kantorovich operators based on shape parameter λ, Adv. Studies: Euro-Tbilisi Math. J. 15 (2022), 151–166, DOI: https://doi.org/10.3251/asetmj/19322008210.
- [15] M. Ayman-Mursaleen, A. Kilicman, and M. Nasiruzzaman, Approximation by q-Bernstein-Kantorovich operators with shifted knots of real parameters, Filomat 36 (2022), 1179–1194, DOI: https://doi.org/10.2298/FIL2204179A.
- [16] Q. B. Cai and R. Aslan, On a new construction of generalized q-Bernstein polynomials based on shape parameter λ, Symmetry 13 (2021), 1919, DOI: https://doi.org/10.3390/sym13101919.
- [17] Q. B. Cai, A. Kiliçman, and M. Ayman-Mursaleen, Approximation properties and q-statistical convergence of Stancu type generalized Baskakov-Szász operators, J. Funct. Spaces 2022 (2022), 2286500, DOI: https://doi.org/10.1155/2022/2286500.
- [18] G. V. Milovanovic, M. Mursaleen, and M. Nasiruzzaman, Modified Stancu type Dunkl generalization of Szász-Kantorovich operators, Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. RACSAM 112 (2018), 135–151, DOI: https://doi.org/10.1007/s13398-016-0369-0.
- [19] M. Mursaleen, M. Nasiruzzaman, and A. Alotaibi, On modified Dunkl generalization of Szász operators via q-calculus, J. Inequal. Appl. 2017 (2017), 38, DOI: https://doi.org/10.1186/s13660-017-1311-5.
- [20] M. Nasiruzzaman and A. F. Aljohani, Approximation by Szász-Jakimovski-Leviatan type operators via aid of Appell polynomials, J. Funct. Spaces 2020 (2020), 9657489, DOI: https://doi.org/10.1155/2020/9657489.
- [21] F. Özger, H. M. Srivastava, and S. A. Mohiuddine, Approximation of functions by a new class of generalized Bernstein-Schurer operators, Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. RACSAM 114 (2020), 173, DOI: https://doi.org/10.1007/s13398-020-00903-6.
- [22] N. Rao, M. Heshamuddin, M. Shadab, and A. Srivastava, Approximation properties of bivariate Szász Durrmeyer operators via Dunkl analogue, Filomat 35 (2021), 4515–4532, DOI: https://doi.org/10.2298/FIL2113515R.
- [23] N. Rao, A. Wafi, and A. M. Acu, q-Szász-Durrmeyer type operators based on Dunkl analogue, Complex Anal. Oper. Theory 13 (2019), 915–934, DOI: https://doi.org/10.1007/s11785-018-0816-3.
- [24] A. Wafi and N. Rao, Szász-Gamma operators based on Dunkl analogue, Iran. J. Sci. Technol. Trans. 43 (2019), 213–223, DOI: https://doi.org/10.1007/s40995-017-0433-4.
- [25] S. A. Mohiuddine and F. Özger, Approximation of functions by Stancu variant of Bernstein-Kantorovich operators based on shape parameter α, Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. RACSAM 114 (2020), 70, DOI: https://doi.org/10.1007/s13398-020-00802-w.
- [26] S. A. Mohiuddine, T. Acar, and A. Alotaibi, Construction of a new family of Bernstein-Kantorovich operators, Math. Methods Appl. Sci. 40 (2017), 7749–7759, DOI: https://doi.org/10.1002/mma.4559.
- [27] S. A. Mohiuddine, T. Acar, and M. A. Alghamdi, Genuine modified Bernstein-Durrmeyer operators, J. Inequal. Appl. 2018 (2018), 104, DOI: https://doi.org/10.1186/s13660-018-1693-z.
- [28] M. Nasiruzzaman, A. Mukheimer, and M. Mursaleen, Approximation results on Dunkl generalization of Phillips operators via q-calculus, Adv. Differ. Equ. 2019 (2019), 244, DOI: https://doi.org/10.1186/s13662-019-2178-1.
- [29] M. Nasiruzzaman and N. Rao, A generalized Dunkl type modifications of Phillips-operators, J. Inequal. Appl. 2018 (2018), 323, DOI: https://doi.org/10.1186/s13660-018-1909-2.
- [30] A. De Sole and V. G. Kac, On integral representation of q-gamma and q-beta functions, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 16 (2005), 11–29.
- [31] A. Alotaibi, M. Nasiruzzaman and M. Mursaleen, Approximation by Phillips operators via q-Dunkl generalization based on a new parameter, J. King Saud Univ.-Sci. 33 (2021), 101413, DOI: https://doi.org/10.1016/j.jksus.2021.101413.
- [32] Md. Nasiruzzaman, K. J. Ansari, and M. Mursaleen, On the parametric approximation results of Phillips operators involving the q-Appell polynomials, J. Sci. Tech. Trans. A Sci. 46 (2022), 251–263, DOI: https://doi.org/10.1007/s40995-021-01219-9.
- [33] F. Altomare, Korovkin type theorems and approximation by positive linear operators, Surv. Approx. Theory 5 (2010), 92–164.
- [34] O. Shisha and B. Bond, The degree of convergence of sequences of linear positive operators, Proc. Nat. Acad. Sci. USA 60 (1968), 1196–1200, DOI: https://doi.org/10.1073/pnas.60.4.1196.
- [35] Ç. Atakut and N. Ispir, Approximation by modified Szász-Mirakjan operators on weighted spaces, Proc. Indian Acad. Sci. Math. Sci. 112 (2002), 571–578, DOI: https://doi.org/10.1007/BF02829690.
- [36] M. A. Ozarslan and H. Aktuğlu, Local approximation for certain King type operators, Filomat 27 (2013), 173–181, DOI: https://doi.org/10.2298/FIL1301173O.
- [37] B. Lenze, On Lipschitz type maximal functions and their smoothness spaces, Nederl. Akad. Indag. Math. 50 (1988), 53–63, DOI: https://doi.org/10.1016/1385-7258(88)90007-8.
- [38] J. Peetre, A theory of interpolation of normed spaces, Noteas de mathematica 39, Instituto de Mathemática Pura e Applicada, Conselho Nacional de Pesquidas, Rio de Janeiro, 1968.
- [39] A. Ciupa, A class of integral Favard-Szász type operators, Stud. Univ. Babeş-Bolyai Math. 40 (1995), 39–47.
Uwagi
PL
Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).
Typ dokumentu
Bibliografia
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Identyfikator YADDA
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