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Lipschitz–Nikolskii Constants for the Trotter–Feller Operator

✍ Scribed by Mi Zhou

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
307 KB
Volume
200
Category
Article
ISSN
0022-247X

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✦ Synopsis

In this paper we determine the Lipschitz᎐Nikolskiı constants for the Trotter᎐Feller operator which contains various well-known operators. As corollaries to our general settings we obtain the Lipschitz᎐Nikolskiı constants for a series ȏf concrete operators including the Bernstein, Szasz, Gamma, Weierstrass, and Baskakov operators, their generalizations such as the Cheney᎐Sharma and Bleimann᎐Butzer᎐Hahn operators, and many others. Our results also improve Rathore's on the Meyer-Konig and Zeller operator and the Gamma operator of Muller as well as Rathore and Singh's on the Post᎐Widder operator. Throughout ẗhe paper the probabilistic method is used intensively while a result in probability theory on normal approximation plays a key role.

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