On new generalized θb-contractions and related fixed point theorems

The manuscript is an extension of the investigations concerning θ -contractions which have been newly proposed in (Jleli and Samet in J. Inequal. Appl. 2014:38, 2014 ). The authors generalize the notion of θ -contractions to the case of nonlinear θ b -contraction mappings and prove multi-valued fixe...

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Published inJournal of inequalities and applications Vol. 2022; no. 1
Main Authors Ali, Amjad, Arshad, Muhammad, Hussain, Aftab, Hussain, Nawab, Alsulami, Saud Mastour
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.12.2022
Springer Nature B.V
Subjects
Analysis
Applications of Mathematics
Differential equations
Fixed points (mathematics)
Fractional calculus
Mathematical functions
Mathematics
Mathematics and Statistics
Metric space
Theorems
Multi-valued maps
b-Bianchini–Grandolfi gauge function
Fixed points
Liouville–Caputo fractional differential equations
Contraction
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Summary:The manuscript is an extension of the investigations concerning θ -contractions which have been newly proposed in (Jleli and Samet in J. Inequal. Appl. 2014:38, 2014 ). The authors generalize the notion of θ -contractions to the case of nonlinear θ b -contraction mappings and prove multi-valued fixed point theorems based on the b -Bianchini–Grandolfi gauge function in b -metric spaces. The manuscript consists of a tangible example which displays the motivation for such investigations. The work is compiled by the application of the proposed nonlinear θ b -contractions to Liouville–Caputo fractional differential equations.
ISSN:1025-5834
1029-242X
DOI:10.1186/s13660-022-02770-8