Bulletin of Pure & Applied Sciences- Mathematics and Statistics
  • Year: 2015
  • Volume: 34e
  • Issue: 1and2

Kth Root transformations for a subclass of analytic functions by komatu integral operator

Department of Mathematics, University Arts & Science College, Warangal, 506009, Telangana, India

*Email: rbsharma@kakatiya.ac.in; rbsharma005@gmail.com

** maroju.hari@gmail.com

Mathematics Subject Classification 2010: Primary 30C45, 30C50; Secondary 30C80

Abstract

We introduce a new subclass of analytic functions using Komatu integral operator and obtain the sharp upper bounds for the coefficient functional |b2k+1b2k+1 | corresponding to the kth 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 derivatives. We obtain the Fekete-Szego inequality for the inverse function and for the function . The results of this paper generalize and unify the work of earlier researchers in this direction.

Keywords

Analytic functions, Fractional derivatives, kth root transformation, Komatu integral operator, Subordination