Current Topics in Pure and Computational Complex Analysis by Santosh Joshi Michael Dorff & Indrajit Lahiri

Author:Santosh Joshi, Michael Dorff & Indrajit Lahiri
Language: eng
Format: epub
Publisher: Springer India, New Delhi

where

and the function q 2 is a convex function and is the best dominant of (6.11).

The next theorem is an analogous result for the corresponding differential superordination:

Theorem 6

[21]Let h 1 be convex in , with , with and . If is univalent in ,

and

then . The function q 1 is convex and is the best subordinant.

Combining the last theorem with the above mentioned Hallenbeck and Ruscheweyh result, we obtain the following differential sandwich-type theorem:

Corollary 1

[21]Let h 1 and h 2 be convex in , with . Let , with , and let the functions q i be defined by

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