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

Abstract

In this study, by using the concepts of subordination, we define a new family RM,N,λ,γ of starlike functions of complex order γ 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 RM,N,λ,γ of starlike functions in U. 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 RM,N,λ,γ of starlike functions. Furthermore, for the inverse function and the logg(z)z 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.

Keywords

• analytic functions
• subordination
• convex and starlike functions
• Fibonacci numbers
• shell-like curve
• cardioid domain