Open AccessLOWER BOUND TO A PROBLEM OF MOCANU ON DIFFERENTIAL SUBORDINATION
Author(s) -
Saminathan Ponnusamy
Publication year - 1997
Publication title -
tamkang journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.324
H-Index - 18
eISSN - 0049-2930
pISSN - 2073-9826
DOI - 10.5556/j.tkjm.27.1996.4344
Subject(s) - mathematics , subordination (linguistics) , combinatorics , alpha (finance) , upper and lower bounds , beta (programming language) , unit (ring theory) , differential (mechanical device) , discrete mathematics , mathematical analysis , physics , statistics , computer science , philosophy , construct validity , linguistics , mathematics education , thermodynamics , programming language , psychometrics
Let $s^*$ denote the family of starlike mappings in the unit disc $\Delta$. Let $\mathcal{R}(\alpha, \beta)$ denote the family of normalized analytic functions in $\Delta$ satisfying the condition Re$(f'(z)+\alpha f''(z))>\beta$, $z \in\Delta$ for some $\alpha > 0$. In this note, among other things, we give a lower bound to the problem of Mocanu aimed at determining $\inf\{\alpha : \mathcal{R}(\alpha,0) \subset S^*\}$.