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Certain Classes of Analytic Functions Related to the Crescent-Shaped Regions

  • R. K. RainaEmail author
  • P. Sharma
  • J. Sokół
Real and Complex Analysis
  • 15 Downloads

Abstract

In this paper, we study certain classes of analytic functions which satisfy a subordination condition and are associated with the crescent-shaped regions. We first give certain integral representations for the functions belonging to these classes and also present a relevant example. Making use of some known lemmas, we derive sufficient conditions for the functions to be in these classes. Some results on coefficient estimates are also obtained.

Keywords

Analytic functions convex functions starlike functions subordination k-uniformly convex k-uniformly starlike 

MSC2010 numbers

30C45 

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Copyright information

© Allerton Press, Inc. 2018

Authors and Affiliations

  1. 1.University of Agriculture and TechnologyUdaipurIndia
  2. 2.University of LucknowLucknowIndia
  3. 3.University of RzeszówRzeszówPoland

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