Sharp Coefficient Bounds for a New Subclass of Starlike Functions of Complex Order γ Associated with Cardioid Domain

• Main Authors: Abubaker, A.A (Author), Al-Shaikh, S.B (Author), Khan, M.F (Author), Matarneh, K. (Author)
• Format: Article
• Language: English
• Published: MDPI 2023
• Subjects: analytic functions; cardioid domain; convex and starlike functions; Fibonacci numbers; shell-like curve; subordination
• Online Access: View Fulltext in Publisher; View in Scopus

 In this study, by using the concepts of subordination, we define a new family (Formula presented.) of starlike functions of complex order (Formula presented.) connected with the cardioid domain. The main contribution of this article consists of the derivations of sharp inequality, considering the functions belonging to the family (Formula presented.) of starlike functions in (Formula presented.). Particularly, sharp bounds of the first two Taylor–Maclaurin coefficients, sharp estimates of the Fekete–Szegö-type functionals, and coefficient inequalities are investigated for this newly defined family (Formula presented.) of starlike functions. Furthermore, for the inverse function and the (Formula presented.) function, we investigate the same types of problems. Several well-known corollaries are also highlighted to show the connections between prior research and the new findings. © 2023 by the authors.