Journal of Applied Mathematics
Volume 2012 (2012), Article ID 407071, 10 pages
http://dx.doi.org/10.1155/2012/407071
Research Article

A Note on tvs-G-Cone Metric Fixed Point Theory

Ing-Jer Lin,1 Chi-Ming Chen,2 Chao-Hung Chen,3 and Tien-Ying Cheng2

1Department of Mathematics, National Kaohsiung Normal University, Taiwan
2Department of Applied Mathematics, National Hsinchu University of Education, Taiwan
3Department of Applied Mathematics, Chung Yuan Christian University, Taiwan

Received 26 April 2012; Accepted 2 July 2012

Academic Editor: Yansheng Liu

Copyright © 2012 Ing-Jer Lin et al. 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

For a tvs-G-cone metric space ( 𝑋 , 𝐺 ) and for the family 𝒜 of subsets of X, we introduce a new notion of the tvs-ℋ-cone metric ℋ with respect to G, and we get a fixed result for the 𝒞 ℬ 𝒲 -tvs-G-cone-type function in a complete tvs-G-cone metric space ( 𝒜 , ℋ ) . Our results generalize some recent results in the literature.