Study of some subclasses of univalent functions and their radius properties

Abstract

An analytic functionfor some l b 0 and m > À1. For À1 a a a 1, we introduce a geometrically motivated S p ðaÞ-class defined by;where S represents the class of all normalized univalent functions in D. In this paper, the authors determine necessary and su‰cient coe‰cient conditions for certain class of functions to be in S p ðaÞ. Also, radius properties are considered for S p ðaÞ-class in the class S. In addition, we also find disks jzj < r :¼ rðl; mÞ for which 1 r f ðrzÞ A Uðl; mÞ whenever f A S. In addition to a number of new results, we also present several new su‰cient conditions for f to be in the class Uðl; mÞ.

Univalence and starlikeness of nonlinear integral transform of certain class of analytic functions

“…Lemma E (Lemma 3 of [18]). Let 0 ≤ μ < 1 and φ(z) = 1 + ∞ n=1 b n z n be a nonvanishing analytic function in satisfying the coefficient condition…”

Some characteristic properties of analytic functions

“…have been studied for µ > −1 in [13] (for −1 < µ < 0 in [9] and for 0 < µ < 1 in [22]). Moreover, for µ = 0, a class involving a certain linear operator under a subordination condition is investigated in [4].…”