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Meromorphic univalent functions with positive coefficients

Published online by Cambridge University Press:  17 April 2009

M.L. Mogra ,
T.R. Reddy  and
O.P. Juneja
M.L. Mogra
Affiliation:
School of Mathematical Sciences, University of Khartoum, Khartoum, SUDAN.
T.R. Reddy
Affiliation:
Department of Mathematics, Indian Institute of Technology, Kanpur-208016, INDIA.
O.P. Juneja
Affiliation:
Department of Mathematics, Kakatiya University, Warangal-506009, AP, INDIA.
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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 2 , October 1985 , pp. 161 - 176
Copyright
Copyright © Australian Mathematical Society 1985

References

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