Subordination by univalent functions

Authors:
Sunder Singh and Ram Singh

Journal:
Proc. Amer. Math. Soc. **82** (1981), 39-47

MSC:
Primary 30C55

DOI:
https://doi.org/10.1090/S0002-9939-1981-0603598-1

MathSciNet review:
603598

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be the class of functions , which are regular and univalently convex in . In this paper we establish certain subordination relations between an arbitrary member of , its partial sums and the functions and . The well-known result that is subordinate to in for every belonging to follows as a particular case from our results. We also improve certain results of Robinson regarding subordination by univalent functions. A sufficient condition for a univalent function to be convex of order is also given.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1981-0603598-1

Keywords:
Regular functions,
univalent,
starlike and convex functions,
subordination,
subordinating factor sequences,
Hadamard product

Article copyright:
© Copyright 1981
American Mathematical Society