Journal of the Ramanujan Mathematical Society
Volume 29, Issue 3, September 2014 pp. 243–251.
Uniform close-to-convexity radius of sections of functions in the close-to-convex
family
Authors:
S. V. Bharanedhar and S. Ponnusamy
Author institution:Indian Statistical Institute (ISI), Chennai Centre, SETS (Society for Electronic Transactions and security), MGR Knowledge City, CIT Campus, Taramani, Chennai 600 113, India
Summary:
The authors consider the class F of normalized functions f
analytic in the unit disk D and satisfying the condition Re (1 +
zf''(z)/f'(z)) > - 1/2, z ∈ D.
Recently, Ponnusamy et al. [12] have
shown that 1/6 is the uniform sharp bound for the radius of
convexity of every section of each function in the class F.
They conjectured that 1/3 is the uniform univalence radius of
every section of f ∈ F. In this paper, we solve this
conjecture
affirmatively.
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