Original scientific paper

Convolution and radius problems of analytic functions associated with the tilted Carathéodory functions

Nak Eun Cho ; Department of Applied Mathematics, Pukyong National University, Busan, South Korea
Sushil Kumar ; Bharati Vidyapeeth’s College of Engineering, Delhi, India
Virendra Kumar ; Department of Mathematics, Ramanujan College, University of Delhi, Kalkaji, Delhi, India
V. Ravichandran ; Department of Mathematics, National Institute of Technology, Tiruchirappalli, Tamil Nadu, India

Abstract

The concept of convolution is applied to investigate some subordination results for the normalized analytic functions whose first derivative belongs to the class of the tilted Carathéodory functions. The sharp radius of starlikeness of order \(\alpha\) of the product of two normalized analytic functions satisfying certain specified conditions is computed. In addition, the various sharp radii constants such as the radius of lemniscate of Bernoulli starlikeness, radius of parabolic starlikeness and several other radius constants of product of two normalized analytic functions are also determined. Relevant connections of our results with the existing results are also pointed out.

Keywords

Starlike function; tilted Carath\(\'\)eodory function; convolution; radius estimate

Hrčak ID:

227061

URI

https://hrcak.srce.hr/227061

Publication date:

25.10.2019.

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