Meir-Keeler-type results on quasi-b_v(s)-metric spaces with new control functions

A contraction mapping is generalized by defining an ambient space under consideration or by altering the contraction condition. In this study, we first define a new space called quasi-b_v(s) metric space and verify that this space is a generalization of b_v(s) metric spaces. We also define a new control function which is a generalization of the altering distance function. Finally, we prove the existence of a fixed point for \xi-generalized Meir-Keeler type contractions on quasi-b_v(s)-metric spaces. Many famous results in the field have been improved, generalized, and unified by the results presented here. The main result is used to drive several corollaries and an example is presented to back up the claim.

Keywords:

Fixed point , Meir-Keleer , quasi-b_v(s)-metric , b_v(s)-left-Cauchy , b_v(s)-right-Cauchy