Non-linear contractions via auxiliary functions and fixed point results with some consequences

In this manuscript, we bring into play the essence of a new class of auxiliary functions, $C$-class functions, and exhibited some fixed point results. Notably, in this draft, we come up with the idea of modified $mathcal{Z}_F$-contractions and enquire the existence and uniqueness of fixed points of such operators in the framework of $theta $-metric spaces. Concerning the interpretation of the achieved results, some non-trivial examples are also studied. From obtained theorems, we derive several related fixed point results in usual metric spaces and $theta $-metric spaces.