Fixed Point Results via Least Upper Bound Property and Its Applications to Fuzzy Caputo Fractional Volterra–Fredholm Integro-Differential Equations
In recent years, complex-valued fuzzy metric spaces (in short CVFMS) were introduced by Shukla et al. (Fixed Point Theory 32 (2018)). This setting is a valuable extension of fuzzy metric spaces with the complex grade of membership function. They also established fixed-point results under contractive...
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| Format: | Article |
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MDPI AG
2021-08-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/16/1969 |
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| author | Humaira Muhammad Sarwar Thabet Abdeljawad Nabil Mlaiki |
| author_facet | Humaira Muhammad Sarwar Thabet Abdeljawad Nabil Mlaiki |
| author_sort | Humaira |
| collection | DOAJ |
| description | In recent years, complex-valued fuzzy metric spaces (in short CVFMS) were introduced by Shukla et al. (Fixed Point Theory 32 (2018)). This setting is a valuable extension of fuzzy metric spaces with the complex grade of membership function. They also established fixed-point results under contractive condition in the aforementioned spaces and generalized some essential existence results in fixed-point theory. The purpose of this manuscript is to derive some fixed-point results for multivalued mappings enjoying the least upper bound property in CVFMS. Furthermore, we studied the existence theorem for a unique solution to the Fuzzy fractional Volterra–Fredholm integro-differential equations (FCFVFIDEs) as an application to our derived result involving the Caputo derivative. |
| first_indexed | 2024-03-10T08:36:48Z |
| format | Article |
| id | doaj.art-2020b4cc9733446fb201c322535d93a2 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T08:36:48Z |
| publishDate | 2021-08-01 |
| publisher | MDPI AG |
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| series | Mathematics |
| spelling | doaj.art-2020b4cc9733446fb201c322535d93a22023-11-22T08:34:36ZengMDPI AGMathematics2227-73902021-08-01916196910.3390/math9161969Fixed Point Results via Least Upper Bound Property and Its Applications to Fuzzy Caputo Fractional Volterra–Fredholm Integro-Differential EquationsHumaira0Muhammad Sarwar1Thabet Abdeljawad2Nabil Mlaiki3Department of Mathematics, University of Malakand, Chakdara Dir(L) 18800, PakistanDepartment of Mathematics, University of Malakand, Chakdara Dir(L) 18800, PakistanDepartment of Medical Research, China Medical University, Taichung 40402, TaiwanDepartment Mathematics and General Sciences, Prince Sultan University, P.O. Box 66833, Riyadh 11586, Saudi ArabiaIn recent years, complex-valued fuzzy metric spaces (in short CVFMS) were introduced by Shukla et al. (Fixed Point Theory 32 (2018)). This setting is a valuable extension of fuzzy metric spaces with the complex grade of membership function. They also established fixed-point results under contractive condition in the aforementioned spaces and generalized some essential existence results in fixed-point theory. The purpose of this manuscript is to derive some fixed-point results for multivalued mappings enjoying the least upper bound property in CVFMS. Furthermore, we studied the existence theorem for a unique solution to the Fuzzy fractional Volterra–Fredholm integro-differential equations (FCFVFIDEs) as an application to our derived result involving the Caputo derivative.https://www.mdpi.com/2227-7390/9/16/1969complex-valued fuzzy metric spacefuzzy mappingsfixed-pointcauchy sequence and contractive conditionleast upper bound property |
| spellingShingle | Humaira Muhammad Sarwar Thabet Abdeljawad Nabil Mlaiki Fixed Point Results via Least Upper Bound Property and Its Applications to Fuzzy Caputo Fractional Volterra–Fredholm Integro-Differential Equations Mathematics complex-valued fuzzy metric space fuzzy mappings fixed-point cauchy sequence and contractive condition least upper bound property |
| title | Fixed Point Results via Least Upper Bound Property and Its Applications to Fuzzy Caputo Fractional Volterra–Fredholm Integro-Differential Equations |
| title_full | Fixed Point Results via Least Upper Bound Property and Its Applications to Fuzzy Caputo Fractional Volterra–Fredholm Integro-Differential Equations |
| title_fullStr | Fixed Point Results via Least Upper Bound Property and Its Applications to Fuzzy Caputo Fractional Volterra–Fredholm Integro-Differential Equations |
| title_full_unstemmed | Fixed Point Results via Least Upper Bound Property and Its Applications to Fuzzy Caputo Fractional Volterra–Fredholm Integro-Differential Equations |
| title_short | Fixed Point Results via Least Upper Bound Property and Its Applications to Fuzzy Caputo Fractional Volterra–Fredholm Integro-Differential Equations |
| title_sort | fixed point results via least upper bound property and its applications to fuzzy caputo fractional volterra fredholm integro differential equations |
| topic | complex-valued fuzzy metric space fuzzy mappings fixed-point cauchy sequence and contractive condition least upper bound property |
| url | https://www.mdpi.com/2227-7390/9/16/1969 |
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