LOWER BOUND TO A PROBLEM OF MOCANU ON DIFFERENTIAL SUBORDINATION
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Abstract
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 $\inf\{\alpha : \mathcal{R}(\alpha,0) \subset S^*\}$.
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References
S. S. Miller and P. T. Mocanu, "Second order differential inequalities in the complex plane," J. Math. Anal. Appl., 65(1978), 289-305.
S. S. Miller and P. T. Mocanu,"Marx-Strohhiicker differential subordinations systems", Proc.Amer. Math. Soc., 99(1987), 527-534.
P. T. Mocanu, "On starlikeness of Libera transform," Mathematica(Cluj), 28(51)(1986), 153-155. [4] S. Ponnusamy, "Differential subordination and starlike functions," Complex variables: Theory and Appln., 19 (1992), 185-194.
S. Ponnusamy, "Differential subordination concerning starlike functions," Internal Report, SPIC Science Foundation, 1990; (Also Proc. Indian Acad. Sci. (Math. Sci.), 104(1994), 397-411).
S. Ponnusamy, "Differential subordination and Bazilevic function," Internal Report, SPIC Science Foundation. 1990; (Also Proc. Indian Acad. Sci. (Math. Sci.), (1995))