K~th ROOT TRANSFORMATIONS FOR A SUBCLASS OF ANALYTIC FUNCTIONS BY KOMATU INTEGRAL OPERATOR

摘要

We introduce a new subclass of analytic functions using Komatu intcgral operator and obtain the sharp upper bounds for the coefficient functional |b_(2k+1) - μ b_(k+1)~2 | corresponding to the k~(th) root transformation for the function f in this class. We also study certain applications of our results for the functions defined through convolution and fractional dcrivatives. We obtain the Fekete- Szego inequality for the inverse function and for the function z/f(z). The results of this paper gencralize and unify the work of earlier researchers in this direction.