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Piggyback-Dualitäten

Published online by Cambridge University Press:  17 April 2009

B.A. Davey  and
H. Werner
B.A. Davey
Affiliation:
Department of Mathematics, La Trobe University, Bundoora, Victoria 3083, Australia
H. Werner
Affiliation:
FB.17 - Mathematik GHK Universität, D-3500 Kassel, West Germany.
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Abstract

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For the class of meromorphically starlike functions of prescribed order, the concept of type has been introduced. A characterization of meromorphically starlike functions of order α and type β has been obtained when the coefficients in its Laurent series expansion about the origin are all positive. This leads to a study of coefficient estimates, distortion theorems, radius of convexity estimates, integral operators, convolution properties et cetera for this class. It is seen that the class considered demonstrates, in some respects, properties analogous to those possessed by the corresponding class of univalent analytic functions with negative coefficients.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 32 , Issue 1 , August 1985 , pp. 1 - 32
Copyright
Copyright © Australian Mathematical Society 1985

References

[1]Baker, K. and Pixley, A.F., “Polynomial interpolation and the Chinese remainder theorem for algebraic systems”, Math. Z. 143 (1975), 165–174.CrossRefGoogle Scholar
[2]Balbes, R., “On free pseudo-complemented and relatively pseudo-complemented semi-lattices”, Fund. Math. 78 (1973), 119–131.CrossRefGoogle Scholar
[3]Davey, B.A., “Topological duality for prevarieties of universal algebras”, Studies in foundations and combinatorics, 61–99 (Advanced in Mathematics: Supplementary Studies, 1. Academic Press, New York, London, 1978).Google Scholar
[4]Davey, B.A., “Duality for equational classes of Brouwerian algebras and Heyting algebras”, Trans. Amer. Math. Soc. 221 (1976), 119–146.CrossRefGoogle Scholar
[5]Davey, B.A., “Dualities for Stone algebras, double Stone algebras and relative Stone algebras”, Colloq. Math. 46 (1982), 1–14.CrossRefGoogle Scholar
[6]Davey, B.A. and Werner, H., “Dualities and equivalences for varieties of algebras”, Contributions to lattice theory, 101–275 (Coll. Math. Soc. János Bolyai, 33. North-Holland, Amsterdam, 1983).Google Scholar
[7]Davey, B.A. and Werner, H., “Piggyback dualities”, (Coll. Math. Soc. János Bolyai (to appear).Google Scholar
[8]Goldberg, M.S., “Distributive Ockham algebras: free algebras and injectivity”, Bull. Austral. Math. Soc. 24 (1981), 161–203.CrossRefGoogle Scholar
[9]Goldberg, M.S., “Topological duality for distributive Ockham algebras”, Studia Logica 42 (1983), 23–31.CrossRefGoogle Scholar
[10]Hofmann, K.H., Mislove, M. and Stralka, A., The Pontryagin duality of compact 0-dimensional semilattices and its applications (Lecture Notes in Mathematics, 396. Springer-Verlag, Berlin, Heidelberg, New York, 1974).CrossRefGoogle Scholar
[11]Priestley, H.A., “Representation of distributive lattices by means of ordered Stone spaces”, Bull. London Math. Soc. 2 (1970), 186–190.CrossRefGoogle Scholar
[12]Priestley, H.A., “Ordered topological spaces and the representation of distributive lattices”, Proc. London Math. Soc. (3) 24 (1972), 507–530.CrossRefGoogle Scholar
[13]Urquhart, A., “Distributive lattices with a dual homomorphic operation”, Studia Logika 38 (1979), 201–209.CrossRefGoogle Scholar