Surveys in Mathematics and its Applications

ISSN1842-6298 (electronic), 1843-7265 (print)

Volume 11 (2016), 11 -- 19

This work is licensed under a Creative Commons Attribution 4.0 International License.## A NEW SUBCLASS OF CLOSE-TO-CONVEX FUNCTIONS

## J. K. Prajapat

Abstract. In this work, we introduce and investigate an interesting subclass X_{t}(γ) of analytic and close-to-convex functions in the open unit disk U. For functions belonging to the class X_{t}(γ), we drive several properties including coefficient estimates, distortion theorems, covering theorems and radius of convexity.2010 Mathematics Subject Classification:30C45

Keywords:Analytic Functions, Univalent Function, Starlike Functions, Close-to-Convex Function

## References

I. Graham, G. Kohr,

Geometric Function Theory in One and Higher Dimensions, Marcel Dekker, Inc. (2003). MR2017933(2004i:32002). Zbi 1042.30001.C.-Y. Gao, S.-Q. Zhou,

On a class of analytic functions related to the class to the starlike functions, Kyungpook Math. J.45(2005), 123-130. MR2142284(2006b:30025). Zbi 1085.30015J. Kowalczyk, E. Les-Bomba,

On a subclass of close-to-convex functions, Appl. Math. Letters23(2010), 1147-1151. MR2665584(2011g:30032). Zbi 1193.30018.Q.-H. Xu, H. M. Srivastava, Z. Li,

A certain subclass of analytic and close-to-convex functions, Appl. Math. Letters24(2011), 396-401. MR2741053 (2011j:30022). Zbi 1206.30035.Z.-G. Wang, D.-Z. Chen,

On a certain subclass of close-to-convex functions, Hacet. J. Math. Stat.38(2)(2009), 95-101. MR2561390. Zbi 1178.30022.

J. K. Prajapat

Department of Mathematics,

Central University of Rajasthan,

Bandarsindri, Kishangarh-305817,

Dist.-Ajmer, Rajasthan, INDIA.

e-mail: jkprajapat@curaj.ac.in

http://wikieducator.org/User:Jkprajapat