Some preservation properties of MKZ-Stancu type operators
DOI:
https://doi.org/10.5644/SJM.10.1.12Keywords:
Function of modulus of continuity, Lipschitz continuous function, Stancu type operatorAbstract
In this work, we construct Stancu type modification of the generalization of Meyer-König and Zeller operators (MKZ) defined in [12]. We show that the Lipschitz constant of a Lipschitz continuous function and the properties of the function of modulus of continuity can be retained by these operators.
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References
B. M. Brown, D. Elliott and D. F. Paget, Lipschitz constants for the Bernstein polynomials of a Lipschitz continuous function, J. Approx. Theory, 49 (2) (1987), 196--199.
İ. Büyükyazii, Approximation by Stancu-Chlodowsky polynomials, Comput. Math. Appl., 59 (1) (2010), 274--282.
Feilong Cao, Chunmei Ding and Zongben Xu, On multivariate Baskakov operators, J. Math. Anal. Appl., 307 (1) (2005), 274--291.
E. W. Cheney and A. Sharma, Bernstein power series, Canad. J. Math., 16 (1964), 241--253.
A. Erençin, H. G. İnce and A. Olgun, A class of linear positive operators in weighted spaces, Math. Slovaca, 62 (1) (2012), 63--76.
Z. Finta, Direct and converse results for Stancu operator, Period. Math. Hungar., 44 (1) (2002), 1--6.
S. G. Gal, Approximation by complex Berstein-Kantorovich and Stancu-Kantorovich polynomials and their iterates in compact disk, Rev. Anal. Numér. Théor. Approx., 37 (2) (2008), 159--168.
M. K. Khan, Approximation properties of Beta operators, Progress in Approximation Theory, (1991), Academic Press, Boston, MA, (1991), 483--495.
Zhongkai Li, Bernstein polynomials and modulus of continuity, J. Approx. Theory, 102 (2000), 171--174.
W. Meyer-König and K. Zeller, Bernsteinsche potenzreihen, Studia Math., 19 (1960), 89--94.
G. Nowak, Approximation properties for generalized q-Bernstein polynomials, J. Math. Anal. Appl., 350 (1) (2009), 50--55.
L. Rempulska and M. Skorupka, Approximation by generalized MKZ-operators in polynomial weighted spaces, Anal. Theory Appl., 23 (1) (2007), 64--75.
D. D. Stancu, Approximation of functions by a new class of linear polynomial operators, Rev. Roumaine Math. Pures Appl., 13 (1968), 1173--1194.
E. I. Stoica-Laze, On the Stancu type linear positive operators of approximation constructed by using the beta and gamma functions, Stud. Univ. Babeş-Bolyai Math., 54 (2)(2009), 117--126.
T. Trif, An Elementary proof of the preservation of Lipschitz constants by the Meyer-König and Zeller operators, J. Inequal. Pure Appl. Math., 4 (5) (2003), Article 90, 3pp.
G. Başcanbaz-Tunca and Y. Tuncer, Some properties of multivariate beta operator, Fasc. Math., 41 (2009), 31--43.
G. Başcanbaz-Tunca and Y. Tuncer, On a Chlodovsky variant of a multivariate beta operator, J. Comput. Appl. Math., 235 (16) (2011), 4816--4824.
G. Başcanbaz-Tunca and F. Taşdelen, On Chlodovsky form of the Meyer-König and Zeller operators, An. Univ. Vest Timiş. Ser. Mat.-Inform., XLIX, 2 (2011), 137--144.
Jiang Yanjie, Li Junming, The rate of convergence of q-Bernstein-Stancu polynomials, Int. J. Wavelets, Multiresol. Info. Proc., 7 (6) (2009), 773--779.
