Recently, Filipovic et al. [M. Filipovic, L. Paunovic, S. Radenovic, M. Rajovic, 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.

A vector metric space is a generalization of a metric space, where the metric is Riesz space valued. We prove some common fixed point theorems for four mappings in ordered vector metric spaces. Obtained results extend and generalize well-known comparable results in the literature.

The main goal of the present paper is to obtain several fixed point theorems in the framework of F-quasi-metric spaces, which is an extension of F-metric spaces. Also, a Hausdorff δ-distance in these spaces is introduced, and a coincidence point theorem regarding this distance is proved. We also present some examples for the validity of the given results and consider an application to the Volterra-type integral equation.