SOME APPLICATIONS OF FRACTIONAL CALCULUS OPERATORS TO THE ANALYTIC PART OF HARMONIC UNIVALENT FUNCTIONS

Recently, Jahangiri [4] studied the harmonic starlike functions of order ®, and he de¯ned the class TH(®) consisting of functions f = h + g, where h and g are the analytic and the co-analytic part of the func-tion f, respectively. In [3] the author introduced the class TH(®; ¯) of analytic functions and he proved various coe±cient inequalities and growth and distortion theorems, and obtained the radius of convexity for the function h if the function f belongs to the classes TH(®) and TH(®; ¯). In this paper, we derive various distortion theorems for the fractional calculus and the fractional integral operator of the function h, the analytic part of the function f, if the function f belongs to the class TH(®; ¯)