A new inner approach for differential subordinations
| Autor: | Adam Lecko |
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| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Proceedings of the Royal Society of Edinburgh: Section A Mathematics. :1-14 |
| ISSN: | 1473-7124 0308-2105 |
| Popis: | 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| 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. |
| Databáze: | OpenAIRE |
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