Inclusion properties for certain subclasses of analytic functions defined by using the generalized Bessel functions

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Authors :

H. M. Srivastavaa K. A. Selvakumaranb and S. D. Purohitc,*

Author Address :

aDepartment of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3R4, Canada.
bDeptartment of Mathematics, R. M. K College of Engineering and Technology, Puduvoyal 601206, Tamil Nadu, India.
cDepartment of Basic Sciences (Mathematics), College of Tech. and Engg., M. P. University of Agriculture and Technology, Udaipur 313001, Rajasthan, India.

*Corresponding author.

Abstract :

By making use of the operator $B_\nu^c$ defined by the generalized Bessel functions of the first kind, the authors introduce and investigate several new subclasses of starlike, convex, close-to-convex and quasi-convex functions. The authors establish inclusion relationships associated with the aforementioned operator. Some interesting corollaries and consequences of the main inclusion relationships are also considered.

Keywords :

Analytic functions; Starlike functions; Convex functions; Close-to-convex functions; Quasi-convex functions; Generalized Bessel functions.

DOI :

Article Info :

Received : January 23, 2015; Accepted : June 12, 2015.