tailieunhanh - Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2010, Article ID 978121,

Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2010, Article ID 978121, 15 pages doi: Research Article Common Fixed Point Results in Metric-Type Spaces ´ ´ Mirko Jovanovic,1 Zoran Kadelburg,2 and Stojan Radenovic3 1 Faculty of Electrical Engineering, University of Belgrade, Bulevar kralja Aleksandra 73, 11000 Beograd, Serbia 2 Faculty of Mathematics, University of Belgrade, Studentski Trg 16, 11000 Beograd, Serbia 3 Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Beograd, Serbia Correspondence should be addressed to Stojan Radenovi´ , sradenovic@ c Received 16 October 2010; Accepted 8 December 2010 Academic Editor: Tomonari Suzuki Copyright q 2010 Mirko Jovanovi´ et. | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2010 Article ID 978121 15 pages doi 2010 978121 Research Article Common Fixed Point Results in Metric-Type Spaces Mirko Jovanovic 1 Zoran Kadelburg 2 and Stojan Radenovic3 1 Faculty of Electrical Engineering University of Belgrade Bulevar kralja Aleksandra 73 11000 Beograd Serbia 2 Faculty of Mathematics University of Belgrade Studentski Trg 16 11000 Beograd Serbia 3 Faculty of Mechanical Engineering University of Belgrade Kraljice Marije 16 11120 Beograd Serbia Correspondence should be addressed to Stojan Radenovic sradenovic@ Received 16 October 2010 Accepted 8 December 2010 Academic Editor Tomonari Suzuki Copyright 2010 Mirko Jovanovic 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. Several fixed point and common fixed point theorems are obtained in the setting of metric-type spaces introduced by M. A. Khamsi in 2010. 1. Introduction Symmetric spaces were introduced in 1931 by Wilson 1 as metric-like spaces lacking the triangle inequality. Several fixed point results in such spaces were obtained for example in 2-4 . A new impulse to the theory of such spaces was given by Huang and Zhang 5 when they reintroduced cone metric spaces replacing the set of real numbers by a cone in a Banach space as the codomain of a metric such spaces were known earlier under the name of K-metric spaces see 6 . Namely it was observed in 7 that if d x y is a cone metric on the set X in the sense of 5 then D x y IId x ỳ II is symmetric with some special properties particularly in the case when the underlying cone is normal. The space X D was then called the symmetric space associated with cone metric space X d . The last observation also led Khamsi 8 to introduce a new type of spaces which he called metric-type spaces .