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Abstract and Applied Analysis
Volume 2014, Article ID 268230, 6 pages
Research Article

Ulam-Hyers Stability and Well-Posedness of Fixed Point Problems for α-λ-Contraction Mapping in Metric Spaces

1Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
2Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, Rangsit Center, Pathum Thani 12121, Thailand

Received 13 January 2014; Revised 27 April 2014; Accepted 22 May 2014; Published 12 June 2014

Academic Editor: Adrian Petrusel

Copyright © 2014 Marwan Amin Kutbi and Wutiphol Sintunavarat. 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 study Ulam-Hyers stability and the well-posedness of the fixed point problem for new type of generalized contraction mapping, so called - -contraction mapping. The results in this paper generalize and unify several results in the literature such as the Banach contraction principle.