Open AccessOn nonlinear fuzzy set-valued $ \Theta $-contractions with applications
Author(s) -
Mohammed Shehu Shagari,
Saima Rashid,
Khadijah M. Abualnaja,
Monairah Alansari
Publication year - 2021
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2021605
Subject(s) - mathematics , complement (music) , fixed point , fuzzy logic , fixed point theorem , nonlinear system , set (abstract data type) , fuzzy set , metric space , binary number , metric (unit) , pure mathematics , discrete mathematics , point (geometry) , algebra over a field , mathematical analysis , computer science , arithmetic , artificial intelligence , geometry , biochemistry , chemistry , physics , operations management , quantum mechanics , complementation , programming language , economics , gene , phenotype
Among various improvements in fuzzy set theory, a progressive development has been in process to investigate fuzzy analogues of fixed point theorems of the classical fixed point results. In this direction, taking the ideas of $ \theta $-contractions as well as Feng-Liu's approach into account, some new fuzzy fixed point results for nonlinear fuzzy set-valued $ \theta $-contractions in the framework of metric-like spaces are introduced in this paper without using the usual Pompeiu-Hausorff distance function. Our established concepts complement, unify and generalize a few important fuzzy and classical fixed point theorems in the corresponding literature. A handful of these special cases of our notions are pointed and analyzed. Some of the main results herein are further applied to derive their analogues in metric-like spaces endowed with partial ordering and binary relations. Comparisons and nontrivial examples are given to authenticate the hypotheses and significance of the obtained ideas.