Journal
BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY
Volume 43, Issue 1, Pages 957-991Publisher
MALAYSIAN MATHEMATICAL SCIENCES SOC
DOI: 10.1007/s40840-019-00784-y
Keywords
Starlike functions; Sigmoid function; Subordination; Radius problems; Coefficient estimates
Categories
Funding
- Council of Scientific and Industrial Research(CSIR) [08/133(0018)/2017-EMR-I]
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Let S-SG* = {f. A : z f' is an element of (z)/f (z) < 2/(1 + e(-z))}. For this class, several radius estimates and coefficient bounds are obtained as well as structural formula, growth theorem, distortion theorem and inclusion relations are established. Further, let p be an analytic function such that p(0) = 1. Sharp bounds on beta is an element of R are determined for various first-order differential subordinations such as 1 + beta zp' (z)/p(k) (z), p(z) + beta zp' ( z)/p(k) (z) < 2/(1 + e(-z)) to imply that p(z) < (1 + Az)/(1 + Bz), where -1 <= B < A <= 1 or root 1 + z and also when the position of dominants is interchanged. Moreover, these results are extended by considering beta to be a complex number.
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