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

Nak Eun Cho; Sushil Kumar; Virendra Kumar; V. Ravichandran

Vol. 24 No. 2 (2019)

Regular Articles

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

Published 2019-07-23

Nak Eun Cho
Sushil Kumar
Virendra Kumar
V. Ravichandran

Nak Eun Cho
Department of Applied Mathematics, Pukyong National University, Busan 48513, South Korea

Sushil Kumar
Bharati Vidyapeeth’s College of Engineering, Delhi–110063, India

Virendra Kumar
Department of Applied Mathematics, Pukyong National University, Busan 48513, South Korea

V. Ravichandran
Department of Mathematics, University of Delhi, Delhi–110007, India Department of Mathematics, NIT Trichy, Tiruchirappalli, Tamil Nadu 620015, India

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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

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