### Journals Information

**
Mathematics and Statistics Vol. 10(3), pp. 582 - 587 DOI: 10.13189/ms.2022.100314 Reprint (PDF) (259Kb) **

## The Radii of Starlikeness for Concave Functions

**Munirah Rossdy ^{1}^{,2}^{,*}, Rashidah Omar ^{2}, Shaharuddin Cik Soh ^{1}**

^{1}Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA, Malaysia

^{2}Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA Sabah Branch, Malaysia

**ABSTRACT**

Let denote the functions' class that is normalized, analytic, as well as univalent in the unit disc given by . Convex, starlike, as well as close-to-convex functions resemble the main subclasses of , expressed by , as well as , accordingly. Many mathematicians have recently studied radius problems for various classes of functions contained in . The determination of the univalence radius, starlikeness, and convexity for specific special functions in is a relatively new topic in geometric function theory. The problem of determining the radius has been initiated since the 1920s. Mathematicians are still very interested in this, particularly when it comes to certain special functions in . Indeed, many papers investigate the radius of starlikeness for numerous functions. With respect to the open unit disc and class , the class of concave functions , known as , is defined. It is identified as a normalised analytic function , which meets the requirement of having the opening angle of at . A univalent function is known as concave provided that is concave. In other words, we have that is also convex. There is no literature to date on determining the radius of starlikeness for concave univalent functions related to certain rational functions, lune, cardioid, and the exponential equation. Hence, by employing the subordination method, we present new findings on determining several radii of starlikeness for different subclasses of starlike functions for the class of concave univalent functions .

**KEYWORDS**

Radius Problems, Radius of Starlikeness, Concave Functions, Starlike Functions, Analytic Univalent Functions

**Cite This Paper in IEEE or APA Citation Styles**

(a). IEEE Format:

[1] Munirah Rossdy , Rashidah Omar , Shaharuddin Cik Soh , "The Radii of Starlikeness for Concave Functions," Mathematics and Statistics, Vol. 10, No. 3, pp. 582 - 587, 2022. DOI: 10.13189/ms.2022.100314.

(b). APA Format:

Munirah Rossdy , Rashidah Omar , Shaharuddin Cik Soh (2022). The Radii of Starlikeness for Concave Functions. Mathematics and Statistics, 10(3), 582 - 587. DOI: 10.13189/ms.2022.100314.