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Coupled coincidence points for two mappings in metric spaces and cone metric spaces

Wei Long1*, Billy E Rhoades2 and Miloje Rajović3

Author Affiliations

1 College of Mathematics and Information Science, Jiangxi Normal University, Nanchang, Jiangxi 330022, People's Republic of China

2 Department of Mathematics, Indiana University, Bloomington, IN 47405-7106, USA

3 Faculty of Mechanical Engineering, University of Kragujevac, Dositejeva 19, 36 000 Kraljevo, Serbia

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Fixed Point Theory and Applications 2012, 2012:66  doi:10.1186/1687-1812-2012-66

Published: 23 April 2012


This article is concerned with coupled coincidence points and common fixed points for two mappings in metric spaces and cone metric spaces. We first establish a coupled coincidence point theorem for two mappings and a common fixed point theorem for two w-compatible mappings in metric spaces. Then, by using a scalarization method, we extend our main theorems to cone metric spaces. Our results generalize and complement several earlier results in the literature. Especially, our main results complement a very recent result due to Abbas et al.