SOME APPROXIMATION RESULTS FOR THE STANCU TYPE Q-BERNSTEIN-SCHURER-KANTOROVICH OPERATORS

TitleSOME APPROXIMATION RESULTS FOR THE STANCU TYPE Q-BERNSTEIN-SCHURER-KANTOROVICH OPERATORS
Publication TypeJournal Article
Year of Publication2016
AuthorsMURSALEEN, M, KHAN, TAQSEER
Secondary TitleCommunications in Applied Analysis
Volume20
Issue2
Start Page187
Pagination22
Date Published06/2016
Type of Workscientific: mathematics
ISSN1083-2564
AMS41A10, 41A25, 41A36
Abstract

In this paper we introduce the Stancu type generalization of the q-Bernstein-Schurer-Kantorovich operators and examine their approximation properties. We investigate the convergence of our operators with the help of the Korovkin’s approximation theorem and examine the convergence of these operators in the Lipschitz class of functions. Finally, we introduce the bivariate analogue of these operators and study some results for the bivariate case.
URLhttp://www.acadsol.eu/en/articles/20/2/2.pdf
DOI10.12732/caa.v20i2.2
Short TitleSOME APPROXIMATION RESULTS
Refereed DesignationRefereed
Full Text

REFERENCES

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[3] P.N. Agarwal, Zolt´an Finta, A Satish Kumar, Bernstein-Schurer-Kantorovich operators based on q-integers, Appl. Math. Comput., 256 (2015), 222-231.
[4] A. Aral, Generalization of Sz´asz-Mirakyan operators based on q-integers, Math. Comput. Modelling, 49 (9-10) (2008), 1052-1062.
[5] A. Aral, V. Gupta, R.P. Agarwal, Applications of q-Calculus in Operator Theory, Springer, New York, 2013.
[6] R.A. DeVore, G.G. Lorentz, Constructive Approximation, Springer, Berlin, 1993.
[7] H. Gauchman, Integral inequalities in q-calculs, Comput. Math. Appl., 47 (2004), 281-300.
[8] F.H. Jackson, On a q-definite integrals, Quart. J. Pure Appl. Math., 41 (1910), 193-203.
[9] A. Lupa¸s, A q-analogue of the Bernstein operator, Rocky Mountain J. Math. 36 5 (2006), 1615-1629.
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[11] C.V. Muraru, Note on q-Bernstein-Schurer operators, Studia Univ. Babe¸s-Bolyai, Mathematica, 56 2 (2011), 489-495.
[12] M. Mursaleen, Asif Khan, H.M. Srivastava, K.S. Nisar, Operators constructed by means of q-Lagrange polynomials and A-statistical approximation, Appl. Math. Comput., 219 (2013), 6911-6918.
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[14] M. Mursaleen, Asif Khan, Statistical approximation properties of modified q-Stancu-Beta operators, Bull. Malays. Math. Sci. Soc.(2), 36 3 (2013), 683-690.
[15] M. Mursaleen, Faisal Khan, Asif Khan, Approximation properties for modified q-BernsteinKantorovich operators, Numer. Funct. Anal. Optim., 36 9 (2015), 1178-1197.
[16] M. Mursaleen, Faisal Khan, Asif Khan, Approximation properties for King’s type modified q-Bernstein-Kantorovich operators, Math. Meth. Appl. Sci., 38 2015, 5242-5252.
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[20] M. Ren, X.M. Zeng, King type modification of q-Bernstein-Schurer operators, Czechoslovak Math. J., 63 138 (2013), 805-817.
[10] S. Marinkovi´c, P. Rajkovi´c, M. Stankovi´c, The inequalities for some types of q-integrals, Comput. Math. Appl., 56 (2008), 2490-2498.
[11] C.V. Muraru, Note on q-Bernstein-Schurer operators, Studia Univ. Babe¸s-Bolyai, Mathematica, 56 2 (2011), 489-495.
[12] M. Mursaleen, Asif Khan, H.M. Srivastava, K.S. Nisar, Operators constructed by means of q-Lagrange polynomials and A-statistical approximation, Appl. Math. Comput., 219 (2013), 6911-6918.
[13] M. Mursaleen, Asif Khan, Generalized q-Bernstein-Schurer operators and some approximation theorems, J. Funct. Spaces, (2013), Article ID 719834, 7 pages.
[14] M. Mursaleen, Asif Khan, Statistical approximation properties of modified q-Stancu-Beta operators, Bull. Malays. Math. Sci. Soc.(2), 36 3 (2013), 683-690.
[15] M. Mursaleen, Faisal Khan, Asif Khan, Approximation properties for modified q-BernsteinKantorovich operators, Numer. Funct. Anal. Optim., 36 9 (2015), 1178-1197.
[16] M. Mursaleen, Faisal Khan, Asif Khan, Approximation properties for King’s type modified q-Bernstein-Kantorovich operators, Math. Meth. Appl. Sci., 38 2015, 5242-5252.
[17] M. Orkc¨u, O. Do˘gru, Statistical approximaion of a kind of Kan ¨ torovich type q-Sz´asz-Mirakjan operators, Nonlinear Anal., 75 5 (2012), 2874-2882.
[18] S. Ostrovska, q-Bernstein polynomials and their iterates, J. Approx. Theory, 123 2 (2003), 232-255.
[19] G.M. Phillips, Bernstein polynomials based on the q-integers, Ann. Numer. Math., 4 (1997), 511-518.
[20] M. Ren, X.M. Zeng, King type modification of q-Bernstein-Schurer operators, Czechoslovak Math. J., 63 138 (2013), 805-817.