논문KCI 등재
Stancu type generalization of modified Gamma operators based on q-integers
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
주제분류수학
초록
In this paper, we propose the Stancu type generalization of a kind of modified $q$-Gamma operators. We estimate the moments of these operators and give the basic convergence theorem. We also obtain the Voronovskaja type theorem. Furthermore, we obtain the local approximation, rate of convergence and weighted approximation for these operators.
Abstract
In this paper, we propose the Stancu type generalization of a kind of modified $q$-Gamma operators. We estimate the moments of these operators and give the basic convergence theorem. We also obtain the Voronovskaja type theorem. Furthermore, we obtain the local approximation, rate of convergence and weighted approximation for these operators.
참고문헌 (22)
- A. Aral, "Application of q-Calculus in Operator Theory" (2013), Springer
- Q. M. Cai, "On the convergence of a kind of a modified q-Gamma operators", J. Comput. Anal. Appl, 15(5), pp.826~832 (2013)
- W. Z. Chen, "On the rate of convergence of the gamma operator for functions of bounded variation", Approx. Theory Appl, 1(5), pp.85~96 (1985)
- R. A. DeVore, "Construtive Approximation" (1993), Springer
- Z. Finta, "Approximation properties of q-Baskakov operators", Cent. Eur. J. Math, 8(1), pp.199~211 (2010)
- N. K. Govil, "q-beta-Száasz-Stancu operators", Advanced Studies in Contemporary Mathematics, 22(1), pp.117~123 (2012), 장전수학회
- V. Gupta, "Convergence Estimates in Approximation Theory. VIII" (2014), Springer
- V. Gupta, "On the rate of approximation by q modified beta operators", J. Math. Anal. Appl, 377(2), pp.471~480 (2011)
- V. Gupta, "On a q-analog of the Baskakov basis fuctions", Russ. J. Math. Phys, 20(3), pp.276~282 (2013)
- V. Kac, "Quantum Calculus, Universitext" (2002), Springer
- H. Karsli, "Rate of convergence of new Gamma type operators for functions with derivatives of bounded variation", Math. Comput. Modelling, 45(5-6), pp.617~624 (2007)
- P. P. Korovkin, "Linear Operators and Approximation Theory" (1960), Hindustan Publ. Corp.
- N. I. Mahmudov, "On q-parametric Sz´asz-Mirakjan operators", Mediterr. J. Math, 7(3), pp.297~311 (2010)
- N. I. Mahmudov, "q-Parametric Bleimann Butzer and Hahn operators", J. Inequal. Appl, 2008, pp.15~ (2008)
- G. M. Phillips, "Bernstein polynomials based on the q-integers The Heritage of P. L. Chebyshew: A Festschrift in honor of the 70th-birthday of Professor T", J. Rivlin, Ann. Numer. Math, 4(1-4), pp.511~518 (1997)
- D. D. Stancu, "Approximation of functions by a new class of linear polynomials operators", Rev. Roumaine Math. Pures Appl, 13(8), pp.1173~1194 (1968)
- V. Totik, "The Gamma operators in Lp spaces", Publ. Math, 32, pp.43~55 (1985)
- T. Trif, "Meyer-K¨onig and Zeller operators based on the q-integers", Rev. Anal. Num´er. Th´eor. Approx, 158, pp.221~229 (2002)
- V. S. Videnskii, "On some class of q-parametric positive operators", Operator Theory:Advances and Application, 158, pp.213~222 (2005)
- X. W. Xu, "Approximation properties of modified Gamma opeartos", J. Math. Anal. Appl, 332(2), pp.798~813 (2007)
- I. Yuksel, "Weighted approximation by a certain family of summation integral-type operators", Comput. Math. Appl, 52(10-11), pp.1463~1470 (2006)
- X. M. Zeng, "Approximation properties of Gamma opeartos", J. Math. Anal. Appl, 311(2), pp.389~401 (2005)
이 간행물의 다른 논문 (27건)
On certain hyperplane arrangements and colored graphs송정민pp. 375-382Global stability of the positive equilibrium of a mathematical model for unstirred membrane reactorsTonghua Zhang, Yongli Songpp. 383-389On the topology of the dual space of crossed product C*-algebras with finite groupsFiruz Kamalovpp. 391-397On a class of Finsler metrics with isotropic Berwald curvatureHongmei Zhupp. 399-416The unit ball of L(2R2h(w))김성근pp. 417-428
