Coupled fixed point analysis in fuzzy cone metric spaces with an application to nonlinear integral equations

In this paper, we introduce the concept of coupled type and cyclic coupled type fuzzy cone contraction mappings in fuzzy cone metric spaces. We establish some coupled fixed point results without the mixed monotone property, and also present some coupled fixed results using the partial order metric i...

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Bibliographic Details
Published inAdvances in difference equations Vol. 2020; no. 1; pp. 1 - 25
Main Authors Chen, Gui-Xiu, Jabeen, Shamoona, Rehman, Saif Ur, Khalil, Ahmed Mostafa, Abbas, Fatima, Kanwal, Arzoo, Ullah, Hayat
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 30.11.2020
Springer Nature B.V
SpringerOpen
Subjects
Analysis
Contraction conditions
Coupled fixed point
Difference and Functional Equations
Fixed points (mathematics)
Functional Analysis
Fuzzy cone metric space
Integral equations
Mathematical analysis
Mathematics
Mathematics and Statistics
Metric space
Nonlinear equations
Ordinary Differential Equations
Partial Differential Equations
Strong coupled fixed point
Strong coupled fixed point
Contraction conditions
47H10
Coupled fixed point
Fuzzy cone metric space
54H25
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Summary:In this paper, we introduce the concept of coupled type and cyclic coupled type fuzzy cone contraction mappings in fuzzy cone metric spaces. We establish some coupled fixed point results without the mixed monotone property, and also present some coupled fixed results using the partial order metric in the said space. We present some strong coupled fixed point theorems using cyclic coupled type fuzzy cone contraction mappings in fuzzy cone metric spaces. Moreover, we present an application of nonlinear integral equations for the existence of a unique solution to support our work.
ISSN:1687-1847
1687-1839
1687-1847
DOI:10.1186/s13662-020-03132-8