Approximation properties of certain summation integral type operators

• Autorzy: Patel P. , Mishra V. N.
• Języki publikacji: EN

Abstrakty

EN

In the present paper, we study approximation properties of a family of linear positive operators and establish direct results, asymptotic formula, rate of convergence, weighted approximation theorem, inverse theorem and better approximation for this family of linear positive operators.

Słowa kluczowe

EN

Bernstein polynomial; Baskakov operators; direct results; asymptotic formula; rate of convergence; weighted approximation theorem; inverse theorem; better approximation

PL

wielomian Bernsteina; operatory Baskakova; wyniki bezpośrednie; formuła asymptotyczna; teoria odwrotna

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2015
• Tom: Vol. 48, nr 1
• Strony: 77--90
• Opis fizyczny: Bibliogr. 20 poz.

Twórcy

autor

Patel P.

• Department of Applied Mathematics & Humanities, Sardar Vallabhbhai National Institute of Technology, Surat-395 007 (Gujarat), India; Department of Mathematics, St. Xavier’s College, Ahmedabad-380 009 (Gujarat), India

autor

Mishra V. N.

• Department of Applied Mathematics & Humanities, Sardar Vallabhbhai National Institute of Technology, Surat-395 007 (Gujarat), India; L. 1627 Awadh Puri Colony Beniganj, Phase -III, Opposite — Industrial Training Institute (I. T. I.), Ayodhya Main Road Faizabad-224 001 (Uttar Pradesh), India

Bibliografia

• [1] A. Aral, V. Gupta, R. P. Agarwal, Applications of q-Calculus in Operator Theory, Springer, 2013.
• [2] R. A. De Vore, G. G. Lorentz, Constructive Approximation, Springer, Berlin, 1993.
• [3] O. Duman, M. A. Ozarslan, Szász–Mirakjan type operators providing a better error estimation, Appl. Math. Lett. 20 (2007), 1184–1188.
• [4] Z. Finta, On converse approximation theorem, J. Math. Anal. Appl. 312(1) (2005), 159–180.
• [5] A. D. Gadzhiev, Theorems of the type of P. P. Korovkin type theorems, Math. Zametki 20(5) (1976), 781–786. Math. Notes, English Translation 20(5–6) (1976), 996–998.
• [6] A. D. Gadjiev, R. O. Efendiyev, E. Ibikli, On Korovkin type theorem in the space of locally integrable functions , Czechoslovak Math. J. 1(128) (2003), 45–53.
• [7] N. K. Govil, V. Gupta, Direct estimates in simultaneous approximation for Durrmeyer type operators, Math. Ineqaul. Appl. 10(2) (2007), 371–379.
• [8] V. Gupta, A note on modified Baskakov type operators, Approx. Theory Appl. (N.S.) 10(3) (1994), 74–78.
• [9] V. Gupta, Approximation for modified Baskakov Durrmeyer type operators, Rocky Mountain J. Math. 39(3) (2009), 1–16.
• [10] V. Gupta, A. Aral, Approximation by q Baskakov-Beta operators, Acta Math. Appl. Sinica 27(4) (2011), 569–580.
• [11] V. Gupta, H. Karsli, Some approximation properties by q-Szasz–Mirakyan–Baskakov–Stancu operators, Lobachevskii J. Math. 33(2) (2012), 175–182.
• [12] V. Gupta, M. A. Noor, M. S. Beniwal, On simultaneous approximation for certain Baskakov Durrmeyer type operators, J. Inequal. Pure Appl. Math. 7 (2006), 1–15.
• [13] B. Ibrahim, Approximation by Stancu–Chlodowsky polynomials, Comput. Math. Appl. 59 (2010), 274–282.
• [14] J. P. King, Positive linear operators which preserves x2, Acta Math. Hungar. 99 (2003), 203–208.
• [15] V. Mishra, P. Patel, Approximation properties of q-Baskakov–Durrmeyer–Stancu operators, Mathematical Sciences 7(1) (2013), 38.
• [16] V. Mishra, P. Patel, Some approximation properties of modified Jain-Beta operators, J. Cal. Var. 2013, (2013), 8 pages.
• [17] M. A. Ozarslan, O. Duman, MKZ type operators providing a better estimation on [1/2,1), Canad. Math. Bull. 50 (2007), 434–439.
• [18] D. D. Stancu, Approximation of function by means of a new generalized Bernstein operator, Calcolo 20(2) (1983), 211–229.
• [19] D. K. Verma, V. Gupta, P. N. Agrawal, Some approximation properties of Baskakov–Durrmeyer–Stancu operators, Appl. Math. Comput. 218 (2012), 6549–6556.
• [20] R. Yadav, Bézier variant of Baskakov-Beta-Stancu operators, Ann. Univ. Ferrara, (2011). DOI 10.1007/s11565-011-0145-1