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

Sarita Agrawal () and Swadesh Kumar Sahoo ()
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Sarita Agrawal: Institute of Mathematics and Applications
Swadesh Kumar Sahoo: Indian Institute of Technology Indore

Indian Journal of Pure and Applied Mathematics, 2021, vol. 52, issue 1, 193-204

Abstract: Abstract In this paper we study sharp estimates of pre-Schwarzian derivatives of functions belonging to the Nehari-type classes by using techniques from differential equations. In the sequel, we also see that a solution of a complex differential equation has a special form in terms of ratio of hypergeometric functions resulting to an integral representation. Finally, we attempt to study those univalent functions in the unit disk for which the image domain is an unbounded John domain.

Keywords: Pre-Schwarzian and Schwarzian derivatives; The Nehari class; Hypergeometric function; Initial value problem; Grönwall’s inequality; John domain; Primary 30C45; Secondary 26D10; 26D20; 30C20; 30C55; 33C05; 34A12 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s13226-021-00070-3

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