On Subclass of Bazilevic Function B1(®), It's Distortion and the Fekete-Szego Problem - Marjono (Pusat Publikasi Ilmiah LPPM Institut Teknologi Sepuluh Nopember, 2006)
In this paper we present the distortion and the Fekete-SzegÄo problem of subclass of Bazilevi·c functions, B1(®). First, we present the result of Singh concerning the sharp value of the coe±cients for B1(®), ja2j, ja3j and ja4j. Second, we give a solution of the Fekete-SzegÄo problem, i.e. an estimate of ja3 ¡ ¹a 2 2j for any real and complex numbers ¹ where a2 and a3 are the coe±cients of functions f in B1(®), where B1(®) is defined by (2), i.e. for each ® > 0 and for z 2 D, Re f 0 (z) f(z) z ®¡1 > 0. These results are sharp for the functions f0 defined by (3) for any real number ¹ which satisfies ¹ < (1 ¡ ®)=2, or ¹ ¸ (4 + 3® + ® )=[2(2 + ®)] and for any complex number ¹ which satisfies j3 + ® ¡ 2¹(2 + ®)j ¸ (1 + ®) 2 . These results are sharp for the functions f1 defined by (4) for the other real and complex numbers ¹. Next, we use similar methods to get estimates for linear expressions involving higher coefficients of function in B1(®).