Rosihan M. Ali,¹ K. G. Subramanian,¹ V. Ravichandran,² and Om P. Ahuja³

Abstract

Let f be a normalized analytic function defined on the unit disk and fλ(z):=(1−λ)z+λf(z) for 0<λ≤1. For α>0, a function f∈𝒮𝒫(α,λ) if zf′(z)/fλ(z) lies in the parabolic region Ω:={w:|w−α|<Re ⁡w+α}. Let 𝒞𝒫(α,λ) be the corresponding class consisting of functions f such that (zf′(z))′/fλ′(z) lies in the region Ω. For an appropriate δ>0, the δ-neighbourhood of a function f∈𝒞𝒫(α,λ) is shown to consist of functions in the class 𝒮𝒫(α,λ).