Properties of Functions Formed Using the Sakaguchi and Gao-Zhou Concept

• Main Authors: Jonathan Aaron Azlan Mosiun, Suzeini Abdul Halim
• Format: Article
• Language: English
• Published: MDPI AG 2020-02-01
• Series: Mathematics
• Subjects: close-to-convex; starlike with respect to n-ply symmetric points; univalent
• Online Access: https://www.mdpi.com/2227-7390/8/3/310

This paper introduces a new class related to close-to-convex functions denoted by <inline-formula> <math display="inline"> <semantics> <msubsup> <mi mathvariant="script">K</mi> <mi>s</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>N</mi> </mrow> </msubsup> </semantics> </math> </inline-formula>. This class is based on combining the concepts of starlike functions with respect to <i>N</i>-ply symmetry points of the order <inline-formula> <math display="inline"> <semantics> <mi>&#945;</mi> </semantics> </math> </inline-formula>, introduced by Chand and Singh; and <inline-formula> <math display="inline"> <semantics> <msubsup> <mi mathvariant="script">K</mi> <mi>s</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </msubsup> </semantics> </math> </inline-formula>, introduced by Wang, Gao, and Yuan, which are generalizations of the classes of functions introduced by Sakaguchi and Gao and Zhou, respectively. We investigate the class for several properties including coefficient estimates, distortion and growth theorems, and the radius of convexity.