Affiliation:
1. Department of Mathematics National Institute of Technology Tiruchirappalli Tamil Nadu India
Abstract
Abstract
For normalized starlike functions f : 𝔻 → ℂ, we consider the analytic functions g : 𝔻 → ℂ defined by g(z) = (1 + z(f″(z))/f′(z))/(zf′(z)/f(z)) and g(z) = (1 − α)(zf′(z))/f(z) + α(1 + (zf″(z))/f′(z)), 0 ≤ α ≤ 1. We determine the largest radius ρ with 0 < ρ ≤ 1 such that g(ρ z) is subordinate to various functions with positive real part.
Reference32 articles.
1. Ali, R. M.—Jain, N. K.—Ravichandran, V.: Radii of starlikeness associated with the lemniscate of Bernoulli and the left-half plane, Appl. Math. Comput. 218(11) (2012), 6557–6565.
2. Arora, K.—Kumar, S. S.: Starlike functions associated with a petal shaped domain, Bull. Korean Math. Soc. 59(4) (2022), 993–1010.
3. Cho, N. E.—Kumar, V.—Kumar, S. S.— Ravichandran, V.: Radius problems for starlike functions associated with the sine function, Bull. Iranian Math. Soc. 45(1) (2019), 213–232.
4. Gandhi, S.: Radius estimates for three leaf function and convex combination of starlike functions. In: Mathematical analysis. I. Approximation theory, Springer Proc. Math. Stat., 306, Springer, Singapore, 2018, pp. 173–184.
5. Gandhi, S.—Ravichandran, V.: Starlike functions associated with a lune, Asian-Eur. J. Math. 10(4) (2017), Art. ID 1750064.