Applications of certain operators to the classes related with generalized Janowski functions

Abstract

Recently, Srivastava and Attiya [H.M. Srivastava and A.A. Attiya, An integral operator associated with the Hurwitz–Lerch Zeta function and differential subordination, Integral Transforms Spec. Funct. 18 (2007), pp. 207–216] introduced a linear integral operator on the class of analytic function associated with Hurwitz–Lerch Zeta function. Using this Srivastava–Attiya operator and generalized Janowski functions, certain classes of analytic functions related with the functions of bounded boundary and bounded radius rotation are introduced and studied. Inclusion results, rate of growth of coefficients, radius problem and behaviour of these classes under certain integral operators are investigated.

Keywords:

• analytic functions
• Hurwitz–Lerch Zeta functions
• Srivastava–Attiya operator
• bounded boundary rotation
• inclusion relation
• generalized Janowski functions
• Schwartz functions

2000 Mathematics Subject Classification :

• 30C45
• 30C50
• 11M35

Acknowledgements

The author would like to thank Prof. H. M. Srivastava for his constructive suggestions and Dr S. M. Junaid Zaidi, Rector CIIT, for his support and providing excellent research facilities.