a new approach to the study of fixed point theorems with w-distances via r-functions

We introduce some new generalization of fixed point theorems in complete metric spaces endowed with w-distances via R-functions. Our results extend many of known fixed point theorems such as Reich type contraction, Geraghty contraction, Meir-Keeler contraction, and Z-contraction. In addition, the result and corollaries show that our approach has a constructive attitude and many known and unknown results can be constructed in such way.