TAILIEUCHUNG - Báo cáo hóa học: "Research Article On Janowski Starlike Functions"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article On Janowski Starlike Functions | Hindawi Publishing Corporation Journal ofInequalities and Applications Volume 2007 Article ID 14630 10 pages doi 2007 14630 Research Article On Janowski Starlike Functions M. Caglar Y. Polatoglu A. Sen E. Yavuz and S. Owa Received 23 June 2007 Accepted 3 October 2007 Recommended by Ram N. Mohapatra For analytic functions f z in the open unit disc U with f 0 0 and f 0 1 applying the fractional calculus for f z a new fractional operator DẦf z is introduced. Further a new subclass tfỵ A B consisting of f z associated with Janowski function is defined. The objective of the present paper is to discuss some interesting properties of the class Í A B . Copyright 2007 M. Caglar et al. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction and preliminaries Let o be the class of analytic functions w z in the open unit disc U z e C I z 1 satisfying w 0 0 and I w z I 1 for all z e U. For arbitrary fixed real numbers A and B which satisfy -1 B A 1 we say that p z belongs to the class A B if 00 p z 1 pnzn n 1 is analytic in U and p z is given by 1 Aw z p z z e U 1 Bw z for some w z e o. This class A B was first introduced by Janowski 1 . Therefore we call f z in the class A B Janowski functions. Further let be class of functions 2 Journal of Inequalities and Applications f z of the form f z z X anzn n 2 which are analytic in U. We recall here the following definitions of the fractional calculus fractional integrals and fractional derivatives given by Owa 2 3 also by Srivastava and Owa 4 . Definition . The fractional integral of order A is defined for f z e by D-Af z VT f ỈI-A dZ A 0 1 h J 0 z - Z where the multiplicity of z - Z A 1 is removed by requiring log z - Z to be real when z - Z 0. Definition . The fractional derivative of order A is defined for f z e by DAf z d dA-1 f z d

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