Coefficient, distortion and growth inequalities for certain close-to-convex functions

Abstract

In the present investigation, certain subclasses of close-to-convex functions are investigated. In particular, we obtain an estimate for the Fekete-Szegö functional for functions belonging to the class, distortion, growth estimates and covering theorems. Mathematics Subject Classification (2010): 30C45, 30C80.

On a subclass of multivalent close to convex functions

“…which was studied recently by Wang and Chen [13] and further for λ = 0, A = 1 − 2γ and B = −1, we obtain the class K s (γ) introduced in [6]. For more details of the related work see [1,2,4,8,12,15].…”

A generalized Bohr-Rogosinski phenomenon

“…where g is some starlike function of order 1/2. In view of the Definition 1.8, the generalized class K s (ψ) was studied by Cho et al [36] and Wang et al [35].…”

Sufficient conditions for strong starlikeness

“…For 0 ≤ β < 1, a function f ∈ A is said to be close-toconvex of order β [10,16] if Re(zf (z)/g(z)) > β for some g ∈ S * (in general, g need not be normalized but we add this extra normalization). More results regarding these classes can be found in [9,12]. Recently, the authors have investigated the sufficient conditions for a function to belong to various subclasses of starlike functions in [20,26,27].…”