GENERALIZATIONS OF THE ALEXANDER INTEGRAL OPERATOR FOR ANALYTIC MULTIVALENT FUNCTIONS

Let T-p,T-n be a subclass of analytic multivalent functions of the form f(z) = z(p) + alpha(p) +n(zp+n) + alpha(p) +n+1 z (p+n+1) +... for every z in the open unit disc U. Applying the fractional calculus (fractional integral and fractional derivative), A (lambda)(p,n) f (z) and A(p,n)(lambda) f(z) which are generalizations of the Alexander integral operator are introduced. The object of present paper is to discuss some interesting properties of A(p,n)(-lambda) f (z) and A(p,n)(-lambda)f (z). Also, some simple examples of results for A-(lambda)(p,n) f(z) and A(p,n)(lambda)f (z) are shown. To give some simple examples is very important for the research of mathematics.