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

Authors : R.k. PANDEY

Pages : 0-0

Doi:10.1501/Commua1_0000000219

View : 7 | Download : 7

Publication Date : 1983-01-01

Article Type : Research Paper

Abstract :In this paper we study some classes namely S* insert ignore into journalissuearticles values(X);, K insert ignore into journalissuearticles values(X);, V insert ignore into journalissuearticles values(8); and S insert ignore into journalissuearticles values(m, M); of functions of the form f insert ignore into journalissuearticles values(z); — z + a2 z2 . . . . regular and univalent in the unit disc D = {z: | z ] < 1} and also a class P insert ignore into journalissuearticles values(p.); of functions of the form p insert ignore into journalissuearticles values(z); — 1 + aL z -a, z2 -J- . . . . regular in D. For suitable restrictipns of real constants a and insert ignore into journalissuearticles values(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 insert ignore into journalissuearticles values( z ); - --------- h insert ignore into journalissuearticles values(t);3 “ ’ finsert ignore into journalissuearticles values(t);a d t 1 L ginsert ignore into journalissuearticles values(z);3 J o J where F e S* insert ignore into journalissuearticles values(Â);. g 6 S* insert ignore into journalissuearticles values(jz); and insert ignore into journalissuearticles values(i); lı £ S insert ignore into journalissuearticles values(m, M); or insert ignore into journalissuearticles values(ii); h e K insert ignore into journalissuearticles values(§); or insert ignore into journalissuearticles values(iii); h Ç V insert ignore into journalissuearticles values(S); or hinsert ignore into journalissuearticles values(z); insert ignore into journalissuearticles values(iv );------S P insert ignore into journalissuearticles values(8);. Our results are sharp and generalize almost ali known results obtained so far in z this direction.
Keywords : Starlikeness, Analytic, Functions