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A new inner approach for differential subordinations
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- Journal:
- Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 154 / Issue 1 / February 2024
- Published online by Cambridge University Press:
- 10 February 2023, pp. 259-272
- Print publication:
- February 2024
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In this paper we introduce and examine the differential subordination of the form
\[ p(z)+zp'(z)\varphi(p(z),zp'(z))\prec h(z),\quad z\in\mathbb{D}:=\{z\in\mathbb{C}:|z|<1\}, \]where $h$
is a convex univalent function with $0\in h(\mathbb {D}).$
The proof of the main result is based on the original lemma for convex univalent functions and offers a new approach in the theory. In particular, the above differential subordination leads to generalizations of the well-known Briot-Bouquet differential subordination. Appropriate applications among others related to the differential subordination of harmonic mean are demonstrated. Related problems concerning differential equations are indicated.
DIFFERENTIAL SUBORDINATIONS FOR CLASSES OF MEROMORPHIC p-VALENT FUNCTIONS DEFINED BY MULTIPLIER TRANSFORMATIONS
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 83 / Issue 3 / June 2011
- Published online by Cambridge University Press:
- 05 April 2011, pp. 353-368
- Print publication:
- June 2011
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