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Abstract and Applied Analysis
Volume 2012, Article ID 413965, 12 pages
http://dx.doi.org/10.1155/2012/413965
Research Article

Coefficient Conditions for Harmonic Close-to-Convex Functions

Department of Mathematics, Kinki University, Higashi-Osaka, Osaka 577-8502, Japan

Received 25 January 2012; Accepted 13 April 2012

Academic Editor: Roman Simon Hilscher

Copyright © 2012 Toshio Hayami. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

New sufficient conditions, concerned with the coefficients of harmonic functions 𝑓 ( 𝑧 ) = ( 𝑧 ) + 𝑔 ( 𝑧 ) in the open unit disk 𝕌 normalized by 𝑓 ( 0 ) = ( 0 ) = ( 0 ) 1 = 0 , for 𝑓 ( 𝑧 ) to be harmonic close-to-convex functions are discussed. Furthermore, several illustrative examples and the image domains of harmonic close-to-convex functions satisfying the obtained conditions are enumerated.