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Open AccessArticle

Subclasses of Starlike and Convex Functions Associated with the Limaçon Domain

1
Department of Mathematics, Payame Noor University, Teheran 19395-3697, Iran
2
Institute of Mathematics, Rzeszow University, Al. Rejtana 16c, PL-35-959 Rzeszów, Poland
*
Author to whom correspondence should be addressed.
Symmetry 2020, 12(6), 942; https://doi.org/10.3390/sym12060942
Received: 7 April 2020 / Revised: 28 April 2020 / Accepted: 11 May 2020 / Published: 3 June 2020
(This article belongs to the Special Issue Symmetry in Geometric Functions and Mathematical Analysis)
Let ST L ( s ) and CV L ( s ) denote the family of analytic and normalized functions f in the unit disk D : = z : | z | < 1 , such that the quantity z f ( z ) / f ( z ) or 1 + z f ( z ) / f ( z ) respectively are lying in the region bounded by the limaçon ( u 1 ) 2 + v 2 s 4 2 = 4 s 2 u 1 + s 2 2 + v 2 , where 0 < s 1 / 2 . The limaçon of Pascal is a curve that possesses properties which qualify it for the several applications in mathematics, statistics (hypothesis testing problem) but also in mechanics (fluid processing applications, known limaçon technology is employed to extract electrical power from low-grade heat, etc.). In this paper we present some results concerning the behavior of f on the classes ST L ( s ) or CV L ( s ) . Some appropriate examples are given. View Full-Text
Keywords: univalent functions; subordination; starlike and convex functions; limaçon of Pascal univalent functions; subordination; starlike and convex functions; limaçon of Pascal
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Masih, V.S.; Kanas, S. Subclasses of Starlike and Convex Functions Associated with the Limaçon Domain. Symmetry 2020, 12, 942.

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