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Journal of Applied Mathematics
Volume 2011, Article ID 327941, 11 pages
Research Article

Some New Fixed-Point Theorems for a ( 𝜓 , 𝜙 )-Pair Meir-Keeler-Type Set-Valued Contraction Map in Complete Metric Spaces

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

Received 25 July 2011; Revised 7 October 2011; Accepted 25 October 2011

Academic Editor: George Jaiani

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.


We obtain some new fixed point theorems for a ( 𝜓 , 𝜙 )-pair Meir-Keeler-type set-valued contraction map in metric spaces. Our main results generalize and improve the results of Klim and Wardowski, (2007).