%0 Journal Article
%T Non-linear contractions via auxiliary functions and fixed point results with some consequences
%J International Journal of Nonlinear Analysis and Applications
%I Semnan University
%Z 2008-6822
%A Chanda, Ankush
%A Dey, Lakshmi Kanta
%A Ansari, Arslan Hojat
%D 2022
%\ 03/01/2022
%V 13
%N 1
%P 2025-2042
%! Non-linear contractions via auxiliary functions and fixed point results with some consequences
%K Fixed point
%K $C$-class function
%K $\mathcal{Z}_{F}$-contraction
%K modified $\mathcal{Z}_F$-contraction
%R 10.22075/ijnaa.2021.22017.2315
%X 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.
%U https://ijnaa.semnan.ac.ir/article_5880_1959641f522318979030492d42bbcd61.pdf