@misc{10481/71719,
year = {2021},
url = {http://hdl.handle.net/10481/71719},
abstract = {Very recently, by considering a self-mapping T on a complete metric space satisfying a
general contractivity condition of the form ψ(d(Tx, Ty)) ≤ ϕ(d(x, y)), Proinov proved some fixedpoint theorems, which extended and unified many existing results in the literature. Accordingly,
inspired by Proinov-type contraction conditions, Roldán López de Hierro et al. introduced a novel
family of contractions in fuzzy metric spaces (in the sense of George and Veeramani), whose main
advantage is the very weak constraints imposed on the auxiliary functions that appear in the
contractivity condition. They also proved the existence and uniqueness of fixed points for the
discussed family of fuzzy contractions in the setting of non-Archimedean fuzzy metric spaces. In this
paper, we introduce a new family of fuzzy contractions based on Proinov-type contractions for which
the involved auxiliary functions are not supposed to satisfy any monotonicity assumptions; further,
we establish some new results about the existence and uniqueness of fixed points. Furthermore, we
show how the main results in the above-mentioned paper can be deduced from our main statements.
In this way, our conclusions provide a positive partial solution to one of the open problems posed
by such authors for deleting or weakening the hypothesis of the nondecreasingness character of the
auxiliary functions.},
organization = {Xiao-lan Liu is partially supported by National Natural Science Foundation of China
(Grant No.11872043), Opening Project of Key Laboratory of Higher Education of Sichuan Province for
Enterprise Internationalization and Internet of Things (Grant No.2020WYJ01), Sichuan Science and
Technology Program (Grant No. 2019YJ0541) and Scientific Research Project of Sichuan University
of Science and Engineering (Grant Nos. 2017RCL54, 2019RC42, and 2019RC08), Opening Project of
Sichuan Province University Key Laboratory of Bridge Non-destruction Detecting and Engineering
Computing (Grant No. 2019QZJ03), Open Fund Project of Artificial Intelligence Key Laboratory
of Sichuan Province (Grant No. 2018RYJ02), Zigong Science and Technology Program (Grant No.
2020YGJC03), 2020 Graduate Innovation Project of Sichuan University of Science and Engineering
(Grant No. y2020078). A.F. Roldán López de Hierro is grateful to Project of Ministerio de Ciencia e
Innovación (Grant No. PID2020-119478GB-I00) and also to Junta de Andalucía of the Andalusian
PAIDI (Grant No. FQM-365). A.F. Roldán López de Hierro is grateful to Project of Ministerio de
Ciencia eInnovación (Grant No. PID2020-119478GB-I00) , Junta de Andalucía of the Andalusian
PAIDI (Grant No. FQM-365) and Program FEDER Andalucía 2014-2020 (Grant No. Project A-FQM170-UGR20).},
publisher = {MDPI},
keywords = {Fuzzy metric space},
keywords = {Fixed point},
keywords = {Proinov-type contraction},
keywords = {Non-Archimedean fuzzy metric space},
title = {A New Approach to Proinov-Type Fixed-Point Results in Non-Archimedean Fuzzy Metric Spaces},
doi = {10.3390/math9233001},
author = {Zhou, Mi and Saleem, Naeem and Liu, Xiaolan and Fulga, Andreea and Roldán López de Hierro, Antonio Francisco},
}