Coupled Fixed-Point Results for $T$-Contractions on Cone Metric Spaces with Applications

The notion of coupled fixed point was introduced in 2006 by Bhaskar and Lakshmikantham. On the other hand, Filipović et al. [M. Filipović et al.,"Remarks on "Cone metric spaces and fixed-point theorems of $T$-Kannan and $T$-Chatterjea contractive mappings"," Math. Comput. Modelling 54, 1467–1472 (2011)] proved several fixed and periodic point theorems for solid cones on cone metric spaces. In this paper we prove some coupled fixed-point theorems for certain $T$-contractions and study the existence of solutions of a system of nonlinear integral equations using the results of our work. The results of this paper extend and generalize well-known comparable results in the literature.