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

Authors : Contents Of Volume 34 Mathematics B. A. FRASİN, B. A. FRASİN

Pages : 1-7

View : 18 | Download : 7

Publication Date : 2005-02-01

Article Type : Research Paper

Abstract :Recently, Jahangiri [4] studied the harmonic starlike functions of order α, and he defined the class THinsert ignore into journalissuearticles values(α); consisting of functions f = h + g¯, where h and g are the analytic and the co-analytic part of the function f, respectively. In [3] the author introduced the class THinsert ignore into journalissuearticles values(α, β); of analytic functions and he proved various coefficient inequalities and growth and distortion theorems, and obtained the radius of convexity for the function h if the function f belongs to the classes THinsert ignore into journalissuearticles values(α); and THinsert ignore into journalissuearticles values(α, β);. 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 THinsert ignore into journalissuearticles values(α, β);.
Keywords : Harmonic, Analytic and univalent functions, Fractional calculus and fractional integral operator, 2000 AMS Classification 30 C 45