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Abstrakty
In this paper, we introduce the q-analogue of the Jakimovski-Leviatan type modied operators introduced by Atakut with the help of the q-Appell polynomials. We obtain some approximation results via the well-known Korovkin’s theorem for these operators. We also study convergence properties by using the modulus of continuity and the rate of convergence of the operators for functions belonging to the Lipschitz class. Moreover, we study the rate of convergence in terms of modulus of continuity of these operators in a weighted space.
Wydawca
Czasopismo
Rocznik
Tom
Strony
175--189
Opis fizyczny
Bibliogr. 34 poz.
Twórcy
autor
- Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India
autor
- Department of Mathematics, Jamia Millia Islamia University, New Delhi 110005, India
autor
- Department of Mathematics, Jamia Millia Islamia University, New Delhi 110005, India
Bibliografia
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- [2] Phillips G. M., Bernstein polynomials based on the q-integers, Ann. Numer. Math., 1997, 4, 511–518.
- [3] Acar T., Asymptotic formulas for generalized Szász-Mirakyan operators, Appl. Math. Comput., 2015, 263, 223-239.
- [4] Acar T., Quantitative q-Voronovskaya and q-Grüss-Voronovskaya-type results for q-Szasz Operators, Georgian Math. J., 2016, 23, 459–468.
- [5] Acar T., (p, q)-Generalization of Szasz-Mirakyan operators, Math. Meth. Appl. Sci., 2016, 39, 2685–2695.
- [6] Mursaleen M., Khan A., Statistical approximation properties of modified q- Stancu-Beta operators, Bull. Malays. Math. Sci. Soc., 2013, 36, 683–690.
- [7] Mursaleen M., Khan A., Generalized q-Bernstein-Schurer operators and some approximation theorems, J. Funct. Spaces Appl., Article ID 719834, Volume 2013, 7 pages.
- [8] Mursaleen M., Khan F., Khan A., Approximation properties for modified q-Bernstein-Kantorovich operators, Numer. Funct. Anal. Optim., 2015, 36, 1178–1197.
- [9] Mursaleen M., Khan F., Khan A., Approximation properties for King’s type modified q-Bernstein-Kantorovich operators, Math. Meth. Appl. Sci., 2015, 38, 5242–5252.
- [10] Mursaleen M., Nasiruzzaman M., Dunkl generalization of Kantorovich type Szasz-Mirakjan operators via q-calculus, Asian-Eur. J. Math., DOI: 10.1142/S1793557117500772.
- [11] Mursaleen M., Nasiruzzaman M., Al-Abied A. A. H., Dunkl generalization of q-parametric Szasz-Mirakjan operators, Int. J. Anal. Appl., 2017, 13, 206–215.
- [12] Srivastava H. M., Mursaleen M., Alotaibi A., Nasiruzzaman M., Al-Abied A. A. H., Some approximation results involving the q-Szász-Mirakjan-Kantorovich type operators via Dunkl’s generalization, Math. Meth. Appl. Sci., DOI:10.1002/mma.4397.
- [13] Ulusoy G., Acar T., q-Voronovskaya Type Theorems for q-Baskakov operators, Math. Meth. Appl. Sci., 2016, 39, 3391–3401.
- [14] Büyükyazıcı İ., Tanberkan H., Serenbay S., Atakut C., Approximation by Chlodowsky type Jakimovski-Leviatan operators, Jour. Comput. Appl. Math., 2014, 259, 153–163.
- [15] Mursaleen M., Ansari K. J., Nasiruzzaman M., Approximation by q-analogue of Jakimovski-Leviatan operators involving q-Appell polynomials, Iranian Jour. Sci. Tech.-A (Sci.) (accepted).
- [16] Keleshteri M. E., Mahmudov N. I., A study on q-Appell polynomials from determinantal point of view, Appl. Math. Comp., 2015, 260, 351–369.
- [17] Atakut C., I. Büyükyazici, Approximation by modied integral type Jakimovski-Leviatan operators, Filomat, 2016, 30, 29–39.
- [18] Choi J., Srivastava H. M., q-Extensions of a multivariable and multiparameter generalization of the Gottlieb polynomials in several variables, Tokyo J. Math., 2014, 37, 111–125.
- [19] Srivastava H. M., Some generalizations and basic (or q-) extensions of the Bernoulli, Euler and Genocchi polynomials, Appl. Math. Inform. Sci., 2011, 5, 390–444.
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- [21] Weisstein E. W., q-Derivative, From Math World-A Wolfram Web Resource; Available online at http://mathworld.wolfram.com/q-Derivative.html.
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- [27] Al-Salam W. A., q-Appell polynomials. Ann. Mat. Pura Appl., 1967, 4, 31–45.
- [28] Gadzhiev A. D., A problem on the convergence of a sequence of positive linear operators on unbounded sets, and theorems that are analogous to P. P. Korovkin’s theorem. Dokl. Akad. Nauk SSSR (Russian), 1974, 218, 1001–1004.
- [29] Gadzhiev A. D., Weighted approximation of continuous functions by positive linear operators on the whole real axis, Izv. Akad. Nauk Azerbaijan. SSR Ser. Fiz.-Tehn. Mat. Nauk (Russian), 1975, 5, 41–45.
- [30] Milovanović G. V., Mursaleen M., Nasiruzzaman M., Modied Stancu type Dunkl generalization of Szász-Kantorovich operators, Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Math. RACSAM, DOI 10.1007/s13398-016-0369-0.
- [31] Wafi A., Rao N., Rai D., Appproximation properties by generalized-Baskakov-Kantrovich-Stancu type operators, Appl. Math. Inform. Sci. Lett., 2016, 4, 111–118.
- [32] Wafi A., Rao N., A generalization of Szász-type operators which preserves constant and quadratic test functions, Cogent Math., 2016, 3, 1227023.
- [33] Korovkin P. P., Linear Operators and Approximation Theory, Hindustan Publ. Co., Delhi 1960.
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Uwagi
PL
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).
Typ dokumentu
Bibliografia
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