Sufficient conditions for starlike and convex functions

Abstract

Abstract. For n ≥ 1, let A denote the class of all analytic functions f in the unit disk ∆ of the form f (z) = z + ∞ k=2 a k z k . For Re α < 2 and γ > 0 given, let P(γ, α) denote the class of all functions f ∈ A satisfying the conditionWe find sufficient conditions for functions in P(γ, α) to be starlike of order β. A generalization of this result along with some convolution results is also obtained.

Region of variability of two subclasses of univalent functions

“…It is known that (see [7,Eq. (16)] and [8]) F 1 ⊂ S * and F 2 ⊂ K. Here K denotes the class of all close-to-convex functions.…”

Norm estimates for convolution transforms of certain classes of analytic functions

“…The class F β and its special case F 1 = F have been studied, for example, in [18][19][20] but for different purposes. In [18,Eq. (16)] it has been shown that if f ∈ F , then one has…”

On a problem of Bharanedhar and Ponnusamy involving planar harmonic mappings

“…In 1995, Ponnusamy and Rajasekaran [13] derived the following starlikeness criterion for analytic functions.…”