Certain subclasses of multivalent analytic functions involving the generalized Srivastava–Attiya operator

Abstract

By making use of the principle of subordination between analytic functions and the generalized Srivastava–Attiya operator, we introduce and investigate some new subclasses of multivalent analytic functions. Such results as inclusion relationships and integral-preserving properties involving these subclasses are proved. Several subordination and superordination results associated with this operator are also derived.

Keywords:

• analytic functions
• multivalent functions
• Hadamard product (or convolution)
• subordination and superordination between analytic functions
• Srivastava–Attiya operator
• generalized Srivastava–Attiya operator

2000 Mathematics Subject Classification :

• Primary: 30C45
• Secondary: 30C80

Acknowledgements

The present investigation was supported by the National Natural Science Foundation under Grants 10671059 and 10771056, and by the Scientific Research Fund of Hunan Provincial Education Department under Grant 08C118 of People's Republic of China. The authors would like to thank Prof. H. M. Srivastava for his careful reading and valuable comments which have essentially improved the presentation of this paper.