UPPER BOUND FOR THIRD HANKEL DETERMINANT OF A CLASS OF ANALYTIC FUNCTIONS

UPPER BOUND FOR THIRD HANKEL DETERMINANT OF A CLASS OF ANALYTIC FUNCTIONS

S. Verma, R. Kumar, G.Murugusundaramoorthy

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Abstract

We establish upper bounds for second Hankel determinant, the Fekete-Szego functional and third Hankel determinant for normalized analytic functions f 2 W ( ; ); W ( ; ) =   f : Re   (1   + 2 ) f(z) z + (  2 )f0(z) + zf00(z)   >     ; where  ;   0 and   < 1. Also, we show that these bounds reduce to the bounds of some well-known classes for particular choices of parameters  ; and  .

Keywords

Analytic functions, Coe cient inequalities, Hankel determinant, Fekete- Szego.