Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-682213120220301Non-linear contractions via auxiliary functions and fixed point results with some consequences20252042588010.22075/ijnaa.2021.22017.2315ENAnkush ChandaDepartment of Mathematics, Vellore Institute of Technology, Vellore, IndiaLakshmi KantaDeyDepartment of Mathematics, National Institute of Technology Durgapur, IndiaArslan HojatAnsariDepartment of Mathematics, Karaj Branch, Islamic Azad University, Karaj, IranJournal Article20201204In 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.https://ijnaa.semnan.ac.ir/article_5880_1959641f522318979030492d42bbcd61.pdf