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Fixed and periodic point theorems for T-contractions on cone metric spaces

Rahimi Hamidreza (Department of Mathematics, Faculty of Science, Islamic Azad University, Central Tehran Branch, Tehran, Iran)
Rhoades B.E. (Department of Mathematics, Indiana University, Bloomington, United States)
Radenović Stojan (Faculty of Mechanical Engineering, University of Belgrade, Beograd)
Rad Soleimani Ghasem (Department of Mathematics, Faculty of Science, Islamic Azad University, Central Tehran Branch, Tehran, Iran)

Recently, Filipović et al. [M. Filipović, L. Paunović, S. Radenović, M. Rajović, Remarks on 'Cone metric spaces and fixed point theorems of T-Kannan and T-Chatterjea contractive mappings', Math. Comput. Modelling. 54 (2011) 1467-1472] proved several fixed and periodic point theorems for solid cones on cone metric spaces. In this paper several fixed and periodic point theorems for T-contraction of two maps on cone metric spaces with solid cone are proved. The results of this paper extend and generalize well-known comparable results in the literature.

Keywords: Cone metric space, Fixed point, Periodic point, Property P, Property Q