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This work relates to multivariate beta operator which is expressed shortly as Bn. We show that the operator preserves Lipschitz constant of a Lipschitz continuous function and semi-additivity of the relevant operand. Furthermore, we provide an r-th order generalisation, Bn (r), of Bn.
Czasopismo
Rocznik
Tom
Strony
31--43
Opis fizyczny
Bibliogr. 17 poz.
Twórcy
autor
autor
- Ankara University, Faculty of Science, Department of Mathematics, Ankara,Turkey, tunca@science.ankara.edu.tr
Bibliografia
- [1] Anastassiou G.A., Gal S.G., Approximation theory. Moduli of continuity and global smoothness preservation, Birkhäuser Boston, Inc., Boston, MA, 2000.
- [2] Abel U., Gupta V., Mohapatra R.N., Local approximation by Beta operators, Nonlinear Anal, 62(1)(2005), 41-52.
- [3] Bloom W.R., Elliot D., The modulus of continuity of the remainder in the approximation of Lipschitz functions, J. Approx. Theory, 31(1981), 59-66.
- [4] Brown B.M., Elliot D., Paget D.F., Lipschitz constants for Bernstein polynomials of a Lipschitz continuous function, J. Approx. Theory, 49(1987), 196-199.
- [5] de la Cal J., Valle A.M., Best constants in global smoothness preservation inequalities for some multivariate operators, J. Approx. Theory, 97(1) (1999), 158-180.
- [6] de la Cal J., Valle A.M., Global smoothness preservation by multivariate Bernstein-type operators, Handbook of analytic-computational methods in applied mathematics, 667-707, Chapman & Hall/CRC, Boca Raton, FL, 2000.
- [7] Feller W., An introduction to probability theory and its applications, Vol. II. Second edition John Wiley & Sons, Inc., New York 1971.
- [8] Khan M.K., Approximation properties of beta operators, Progress in approximation theory, Academic Press, Boston, MA., (1991), 483-495.
- [9] Khan M.K., Peters M.A., Lipschitz constants for some approximation operators of a Lipschitz continuous function, J. Approx. Theory, 59(3) (1989), 307-315.
- [10] Khan M.K., Della Vecchia B., Fassih A., On the monotonicity of positive linear operators, J. Approx. Theory, 92(1)(1998), 22-37.
- [11] Kirov G., Popova L., A generalization of the linear positive operators, Math. Balkanica, (N.S.) 7(2)(1993), 149-162.
- [12] Li Z., Bernstein polynomials and modulus of continuity, J. Approx. Theory, 102(1)(2000), 171-174.
- [13] Lupaş A., Die Falge der Beta operatorem, Dissertation, Universitat Stuttgart, 1972.
- [14] Timan A. P., The Theory of Approximation of the Functions of Real Variables, Phizmatgiz, 1960.
- [15] Upreti R., Approximation properties of beta operators, J. Approx. Theory, 45(2)(1985), 85-89.
- [16] Volkov V.I., On the convergence of sequences of linear positive operators in the space of continuous functions of two variables, (Russian), Dokl. Akad. Nauk SSSR, (N.S.) 115(1957), 17-19.
- [17] Wilks S.S., Mathematical Statistics, Wiley, New-York, 1963.
Typ dokumentu
Bibliografia
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bwmeta1.element.baztech-article-BPP2-0014-0038