2021/01/05 by Shalu Yadav, Yadav, Shalu, Kanika Sharma +3
Materials Science · Mathematics · #30C45 #30C80 #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Polymer Synthesis and Characterization
paper · pdf · doi:10.48550/arxiv.2101.01627
openalex publication_date 2021/01/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A starlike univalent function f is characterized by the function zf'(z)/f(z); several subclasses of these functions were studied in the past by restricting the function zf'(z)/f(z) to take values in a region Ω on the right-half plane, or, equivalently, by requiring the function zf'(z)/f(z) to be subordinate to the corresponding mapping of the unit disk \mathbbD to the region Ω. The mappings w1(z):=z+√(1+z2), w2(z):=√(1+z) and w3(z):=ez maps the unit disk \mathbbD to various regions in the right half plane. For normalized analytic functions f satisfying the conditions that f(z)/g(z), g(z)/zp(z) and p(z) are subordinate to the functions wi, i=1,2,3 in various ways for some analytic functions g(z) and p(z), we determine the sharp radius for them to belong to various subclasses of starlike functions.