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Accessible Unlicensed Requires Authentication Published by De Gruyter July 19, 2019

A subclass of uniformly convex functions and a corresponding subclass of starlike function with fixed coefficient associated with q-analogue of Ruscheweyh operator

Shahid Khan, Saqib Hussain, Muhammad A. Zaighum and Maslina Darus
From the journal Mathematica Slovaca

Abstract

Making use of Ruscheweyh q-differential operator, we define a new subclass of uniformly convex functions and corresponding subclass of starlike functions with negative coefficients. The main object of this paper is to obtain, coefficient estimates, closure theorems and extreme point for the functions belonging to this new class. The results are generalized to families with fixed finitely many coefficients.

MSC 2010: Primary 30C45; 30C50

  1. (Communicated by Stanisława Kanas)

Acknowledgement

The authors would like to thank the Editor and referees for their valuable comments which helped to improve the manuscript. The 4th author is supported by UKM grant: GUP-2017-064.

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Received: 2018-08-25
Accepted: 2018-12-19
Published Online: 2019-07-19
Published in Print: 2019-08-27

© 2019 Mathematical Institute Slovak Academy of Sciences