Abstract. The estimate of third Hankel determinantof the analytic function f (z) = z + a 2 z 2 + a 3 z 3 + · · · , for which ℜ(1 + zf ′′ (z)/f ′ (z)) > −1/2 are investigated. The corrected version of a known results [2, Theorem 3.1 and Theorem 3.3] are also obtained.
In the present work, Mittag-Leffler functions with its normalization are
considered. Several results are obtained so that these functions have
certain geometric properties including starlikeness, convexity,
close-to-convexity of order ?, and radius of starlikeness of order ?.
Furthermore, we obtain certain condition so that the normalized Mittag-Leffler
functions belongs to the Hardy space and to the class of bounded analytic
functions. Results obtained are new and their usefulness are depicted by
deducing several interesting corollaries and examples.
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