Creating new contractive mappings to obtain fixed points and data-dependence results under auxiliary functions

This manuscript is concerned with obtaining results for fixed points that arise from new contractive mappings on controlled metric spaces. These mappings are a mixture of Wardowski’s contractions with both multivalued, nonlinear mappings and auxiliary functions. It is also proved that the obtained fixed-point outcomes are well-posed. Additionally, a data-dependence result for fixed points is given. To aid with understanding, several illustrative examples are also provided. Numerous findings that are currently in the literature are specific instances of the findings that were made.