RADII OF ANALYTIC FUNCTIONS SATISFYING SOME COEFFICIENT INEQUALITIES
By
Rajni Mendiratta and Hiten Bansal
Department of Mathematics, Keshav Mahavidyalaya, University of Delhi, Delhi, India-110034
Email: rajni.mendiratta@keshav.du.ac.in, hitenbansal212004@gmail.com
(Received: March 10, 2026; In format: March 24, 2026; Revised: April 10, 2026; Accepted: May 28, 2026)
DOI: https://doi.org/10.58250/jnanabha.2026.56110
Abstract
Let g(z) = z + Σn=2∞ anzn is an analytic function defined on an open unit disc in complex plane with center at origin and radius 1. The a2 coefficient is such that |a2| = 2b, where b ∈ [0, 1], for other coefficients |an| ≤ C/n3 (C > 0) and |an| ≤ cn + d/n(c, d > 0). Optimum or extreme values of radius are evaluated for functions to have convexity of order α(0 ≤ α < 1) and starlikeness of order α, where α ∈ [0, 1[. Radius values for few other properties are also evaluated.
2020 Mathematical Sciences Classification: 30C45, 30C80.
Keywords and Phrases: Starlike Functions, Convex functions, Uniformly Convex functions, Parabolic starlike functions, Radius problems, Constant Initial Coefficient