On the Radius of Starlikeness of certain Analytic Functions with integral Representation

Abstract

In this paper we study some classes namely S* (X), K (X), V (8) and S (m, M) of functions of the form f (z) — z + a2 z2 . . . . regular and univalent in the unit disc D = {z: | z ] < 1} and also a class P (p.) of functions of the form p (z) — 1 + aL z -a, z2 -J- . . . . regular in D. For suitable restrictipns of real constants a and (3 we obtain the radius of starlikeness of order 7) of normalized analytic functions f in D defined by the general integral operatör of the form r a + p rz - ı l /a, F ( z ) - --------- h (t)3 “ ’ f(t)a d t 1 L g(z)3 J o J where F e S* (Â). g 6 S* (jz) and (i) lı £ S (m, M) or (ii) h e K (§) or (iii) h Ç V (S) or h(z) (iv )------S P (8). Our results are sharp and generalize almost ali known results obtained so far in z this direction.

Keywords

• Starlikeness
• Analytic
• Functions

References

1. Communications, Series A1:Mathematics and Statistics