Mizoguchi-Takahashi-type theorems in tvs-cone metric spaces
1 Department of Mathematics, Hashemite University Zarqa, Jordan
2 University of Belgrade, Faculty of Economics, Kamenička 6, 11000 Beograd, Serbia
3 University of Belgrade, Faculty of Mechanical Engineering, Kraljice Marije 16, 11 120 Beograd, Serbia
4 Department of Mathematical Sciences, UAEU, 17551 Al-Ain, United Arab Emirates
Fixed Point Theory and Applications 2012, 2012:106 doi:10.1186/1687-1812-2012-106Published: 25 June 2012
In this paper, the concepts of a set-valued contraction of Mizoguchi-Takahashi type in the context of topological vector space (tvs)-cone metric spaces are introduced and a fixed point theorem in the context of tvs-cone metric spaces with respect to a solid cone is proved. We obtained results which extend and generalize the main results of S. H. Cho with J. S. Bae, Mizoguchi with Takahashi and S. B. Nadler Jr. Two examples are given to illustrate the usability of our results.
2010 MSC: 47H10, 54H25.