About Coupled Points Via Certain Distances

In this study various theorems of fixed points and coupled points are given for some classes of contractive mappings.These results are included in three pivots. Firstly, commute concept and it's a generalization are used to prove the existence common fixed, coincidence coupled, fixed and coupled fixed points in complete g_s-m spaces. Secondly, a new class of mappings are defined namely, ¿-total weakly contraction (and ¿-T-total weakly contraction). Also, the properties of mixed monotone and T-mixed monotone are employed to prove other results in ordered g_s-m spaces.Thirdly, for the first time are dealt with ¿-distance with respect to g_s-m spaces to present some theorems about coupled coincidence, common coupled, fixed and coupled fixed points for all previous classes.