On nonlinear fuzzy set-valued $ \Theta $-contractions with applications

Mohammed Shehu Shagari; Saima Rashid; Khadijah M. Abualnaja; Monairah Alansari; Mohammed Shehu Shagari; Saima Rashid; Khadijah M. Abualnaja; Monairah Alansari

doi:10.3934/math.2021605

AIMS Mathematics

2021, Volume 6, Issue 10: 10431-10448. doi: 10.3934/math.2021605

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Research article

On nonlinear fuzzy set-valued $ \Theta $-contractions with applications

1.
Department of Mathematics, Faculty of Physical Sciences, Ahmadu Bello University, Zaria, Nigeria
2.
Department of Mathematics, Government College University, Faisalabad, Pakistan
3.
Department of Mathematics, Faculty of Science, Taif University, P. O. Box 11099, Taif 21944, Saudi Arabia
4.
Department of Mathematics, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia

Received: 13 December 2020 Accepted: 01 July 2021 Published: 19 July 2021
MSC : 46S40, 47H10

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.
- fixed point,
- fuzzy set,
- fuzzy set-valued map,
- metric-like space,
- multivalued mapping,
- $ \theta $-contraction
Citation: Mohammed Shehu Shagari, Saima Rashid, Khadijah M. Abualnaja, Monairah Alansari. On nonlinear fuzzy set-valued $ \Theta $-contractions with applications[J]. AIMS Mathematics, 2021, 6(10): 10431-10448. doi: 10.3934/math.2021605

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Abstract

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.

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