@misc{10481/76374,
year = {2022},
month = {6},
url = {http://hdl.handle.net/10481/76374},
abstract = {In recent years, Fixed Point Theory has achieved great importance within Nonlinear Analysis
especially due to its interesting applications in real-world contexts. Its methodology
is based on the comparison between the distances between two points and their respective
images through a nonlinear operator. This comparison is made through contractive conditions
involving auxiliary functions whose role is increasingly decisive, and which are acquiring
a prominent role in Functional Analysis. Very recently, Proinov introduced new fixed point
results that have very much attracted the researchers’ attention especially due to the extraordinarily
weak conditions on the auxiliary functions considered. However, one of them, the
nondecreasing character of the main function, has been used for many years without the
chance of being replaced by another alternative property. In this way, several researchers
have recently raised this question as an open problem in this field of study. In order to face
this open problem, in this work we introduce a novel class of auxiliary functions that serve to
define contractions, both in metric spaces and in fuzzy metric spaces, which, in addition to generalizing to Proinov contractions, avoid the nondecreasing character of themain auxiliary
function. Furthermore, we present these new results in the setting of fuzzy metric spaces that
satisfy the conditionNC, which open new possibilities in the metric theory compared to classic
non-Archimedean fuzzy metric spaces. Finally, we include some illustrative examples to
show how to apply the novel theorems to cases that are not covered by other previous results.},
organization = {Universidad de Granada / CBUA},
publisher = {Springer},
keywords = {Fixed point},
keywords = {Fuzzy metric space},
keywords = {Contractivity condition},
keywords = {Property NC},
keywords = {Proinov theorem},
title = {Extended Proinov X-contractions in metric spaces and fuzzy metric spaces satisfying the property NC by avoiding the monotone condition},
doi = {10.1007/s13398-022-01268-8},
author = {Karapinar, Erdal and Roldán López de Hierro, Antonio Francisco},
}