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 exhibit some fixed point results. Notably, in this article, we come up with the idea of modified 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.