Nehari's univalence criteria, pre-Schwarzian derivative and applications

DOI10.1007/s13226-021-00070-3zbMath1473.30006arXiv2004.10417OpenAlexW3166688096MaRDI QIDQ2241680

Swadesh Kumar Sahoo, Sarita Agrawal

Publication date: 9 November 2021

Published in: Indian Journal of Pure \& Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2004.10417

zbMATH Keywords

initial value problemhypergeometric functionJohn domainGrönwall's inequalityNehari classpre-Schwarzian and Schwarzian derivatives

Mathematics Subject Classification ID

Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations (34A12) Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) (30C45) Conformal mappings of special domains (30C20) Classical hypergeometric functions, ({}_2F_1) (33C05) Inequalities involving derivatives and differential and integral operators (26D10) Other analytical inequalities (26D20) General theory of univalent and multivalent functions of one complex variable (30C55)

Cites Work

• On the Nehari univalence criterion and quasicircles
• John disks
• Norm estimates for the Alexander transforms of convex functions of order alpha
• Ahlfors-Weill extensions of conformal mappings and critical points of the Poincaré metric
• Mapping properties of hypergeometric functions and convolutions of starlike or convex functions of order \(\alpha\)
• Rotation and strain
• Injectivity theorems in plane and space
• The Schwarzian derivative and schlicht functions
• Some Criteria of Univalence
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