Development of Fixed Point Results for <i>α</i><sub>Γ</sub>-<i>F</i>-Fuzzy Contraction Mappings with Applications
This manuscript contains several fixed point results for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>α</mi><mo>Γ</mo></msub></semantics></math></inline-...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-06-01
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| Series: | Symmetry |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-8994/15/7/1300 |
| _version_ | 1797587472744448000 |
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| author | Salvatore Sessa Fahad Jahangeer Doha A. Kattan Umar Ishtiaq |
| author_facet | Salvatore Sessa Fahad Jahangeer Doha A. Kattan Umar Ishtiaq |
| author_sort | Salvatore Sessa |
| collection | DOAJ |
| description | This manuscript contains several fixed point results for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>α</mi><mo>Γ</mo></msub></semantics></math></inline-formula>-<i>F</i>-fuzzy contractive mappings in the framework of orthogonal fuzzy metric spaces. The symmetric property guarantees that the distance function is consistent and does not favour any one direction in orthogonal fuzzy metric spaces. No matter how the points are arranged, it enables a fair assessment of the separations between all of them. In fixed point results, the symmetry condition is preserved for several types of contractive self-mappings. Moreover, we provide several non-trivial examples to show the validity of our main results. Furthermore, we solve non-linear fractional differential equations, the Atangana–Baleanu fractional integral operator and Fredholm integral equations by utilizing our main results. |
| first_indexed | 2024-03-11T00:36:31Z |
| format | Article |
| id | doaj.art-c1995bd620234211a58c59c5fe6de916 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-11T00:36:31Z |
| publishDate | 2023-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-c1995bd620234211a58c59c5fe6de9162023-11-18T21:33:10ZengMDPI AGSymmetry2073-89942023-06-01157130010.3390/sym15071300Development of Fixed Point Results for <i>α</i><sub>Γ</sub>-<i>F</i>-Fuzzy Contraction Mappings with ApplicationsSalvatore Sessa0Fahad Jahangeer1Doha A. Kattan2Umar Ishtiaq3Dipartimento di Architettura, Università Dinapoli Federico II, Via Toledo 403, 80121 Napoli, ItalyDepartment of Mathematics and Statistics, International Islamic University Islamabad, Islamabad 44000, PakistanDepartment of Mathematics, Faculty of Sciences and Arts, King Abdulaziz University, Rabigh 21589, Saudi ArabiaOffice of Research, Innovation and Commercialization, University of Management and Technology, Lahore 54770, PakistanThis manuscript contains several fixed point results for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>α</mi><mo>Γ</mo></msub></semantics></math></inline-formula>-<i>F</i>-fuzzy contractive mappings in the framework of orthogonal fuzzy metric spaces. The symmetric property guarantees that the distance function is consistent and does not favour any one direction in orthogonal fuzzy metric spaces. No matter how the points are arranged, it enables a fair assessment of the separations between all of them. In fixed point results, the symmetry condition is preserved for several types of contractive self-mappings. Moreover, we provide several non-trivial examples to show the validity of our main results. Furthermore, we solve non-linear fractional differential equations, the Atangana–Baleanu fractional integral operator and Fredholm integral equations by utilizing our main results.https://www.mdpi.com/2073-8994/15/7/1300fixed pointfuzzy metric spacesintegral equationsAtangana–Baleanu fractional integral operator |
| spellingShingle | Salvatore Sessa Fahad Jahangeer Doha A. Kattan Umar Ishtiaq Development of Fixed Point Results for <i>α</i><sub>Γ</sub>-<i>F</i>-Fuzzy Contraction Mappings with Applications Symmetry fixed point fuzzy metric spaces integral equations Atangana–Baleanu fractional integral operator |
| title | Development of Fixed Point Results for <i>α</i><sub>Γ</sub>-<i>F</i>-Fuzzy Contraction Mappings with Applications |
| title_full | Development of Fixed Point Results for <i>α</i><sub>Γ</sub>-<i>F</i>-Fuzzy Contraction Mappings with Applications |
| title_fullStr | Development of Fixed Point Results for <i>α</i><sub>Γ</sub>-<i>F</i>-Fuzzy Contraction Mappings with Applications |
| title_full_unstemmed | Development of Fixed Point Results for <i>α</i><sub>Γ</sub>-<i>F</i>-Fuzzy Contraction Mappings with Applications |
| title_short | Development of Fixed Point Results for <i>α</i><sub>Γ</sub>-<i>F</i>-Fuzzy Contraction Mappings with Applications |
| title_sort | development of fixed point results for i α i sub γ sub i f i fuzzy contraction mappings with applications |
| topic | fixed point fuzzy metric spaces integral equations Atangana–Baleanu fractional integral operator |
| url | https://www.mdpi.com/2073-8994/15/7/1300 |
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