Journal of Applied Mathematics
Volume 2011 (2011), Article ID 127521, 14 pages
http://dx.doi.org/10.1155/2011/127521
Research Article

Common Fixed Point Theorems of the Asymptotic Sequences in Ordered Cone Metric Spaces

Chi-Ming Chen

Department of Applied Mathematics, National Hsinchu University of Education, Hsinchu 300, Taiwan

Received 13 July 2011; Accepted 20 October 2011

Academic Editor: Yansheng Liu

Copyright © 2011 Chi-Ming Chen. 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

We introduce the notions of the asymptotic 𝒮 ℳ 𝒦 -sequence with respect to the stronger Meir-Keeler cone-type mapping 𝜉 ∶ i n t ( 𝑃 ) ∪ { 𝜃 } → [ 0 , 1 ) and the asymptotic 𝒲 ℳ 𝒦 -sequence with respect to the weaker Meir-Keeler cone-type mapping 𝜙 ∶ i n t ( 𝑃 ) ∪ { 𝜃 } → i n t ( 𝑃 ) ∪ { 𝜃 } and prove some common fixed point theorems for these two asymptotic sequences in cone metric spaces with regular cone 𝑃 . Our results generalize some recent results.