On grounds of the notion of simulation functions, in this manuscript, we bring in the concept of an extended CF-simulation function and conceive a few common fixed point results via such kind of contractions on complete metric spaces. These class of auxiliary functions generalize, improve and extend those of simulation functions, extended simulation functions and CF-simulation functions. However, as applications of the aforesaid results, we figure out some related consequences of it on the said spaces. Our findings are authenticated by the aid of some competent, non-trivial and constructive examples.

This Special Issue of Axioms, titled “Trends in Fixed Point Theory and Fractional Calculus”, presents a collection of ten high-quality papers reflecting the latest developments in two intertwined areas of modern mathematical analysis