Classes of analytic functions with fractional powers defined by means of a certain linear operator

Abstract

Motivated by the success of the familiar Dziok–Srivastava convolution operator, we introduce here a closely-related linear operator for analytic functions with fractional powers. By means of this linear operator, we then define and investigate a class of analytic functions. Finally, we determine certain conditions under which the partial sums of the linear operator of bounded turning are also of bounded turning. We also illustrate an application of a fractional integral operator.

Keywords:

• analytic functions
• fractional powers
• Hadamard product (or convolution)
• subordination between analytic functions
• univalent functions
• convex functions
• close-to-convex functions
• partial sums
• Dziok–Srivastava linear operator
• bounded turning
• generalized hypergeometric function
• fractional integral operator
• Laplace transform
• Cesàro means
• Fox–Wright hypergeometric function

2010 Mathematics Subject Classification :

• Primary: 30C45
• 30C50
• 33C20
• Secondary: 26A33
• 33B15

Acknowledgements

The present investigation was supported, in part, by MOHE under Grant UKM-ST-06-FRGS0107-2009.