Numerical Algorithm for Coupled Fixed Points in Normed Spaces with Applications to Fractional Differential Equations and Economics
This paper introduces interpolative enriched cyclic Reich–Rus–Ćirić operators in normed spaces, expanding existing contraction principles by integrating interpolation and cyclic conditions. This class of operators addresses mappings with discontinuities or non-self mappings, enhancing the applicabil...
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| Format: | Article |
| Language: | English |
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MDPI AG
2025-01-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/9/1/37 |
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| author | Lifang Guo Salha Alshaikey Abeer Alshejari Muhammad Din Umar Ishtiaq |
| author_facet | Lifang Guo Salha Alshaikey Abeer Alshejari Muhammad Din Umar Ishtiaq |
| author_sort | Lifang Guo |
| collection | DOAJ |
| description | This paper introduces interpolative enriched cyclic Reich–Rus–Ćirić operators in normed spaces, expanding existing contraction principles by integrating interpolation and cyclic conditions. This class of operators addresses mappings with discontinuities or non-self mappings, enhancing the applicability of fixed-point theory to more complex problems. This class of operators expands on existing cyclic contractions, including interpolative Kannan mappings, interpolative Reich–Rus–Ćirić contractions, and other known contractions in the literature. We demonstrate the existence and uniqueness of fixed points for these operators and provide an example to illustrate our findings. Moreover, we discuss the applications of our results in solving nonlinear integral equations. Furthermore, we introduce the idea of a coupled interpolative enriched cyclic Reich–Rus–Ćirić operator and establish the existence of a strongly coupled fixed-point theorem for this contraction. Finally, we provide an application to fractional differential equations to show the validity of the main result. |
| format | Article |
| id | doaj-art-af30ed34b12b463c8fc7221e05d1c353 |
| institution | Kabale University |
| issn | 2504-3110 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj-art-af30ed34b12b463c8fc7221e05d1c3532025-01-24T13:33:27ZengMDPI AGFractal and Fractional2504-31102025-01-01913710.3390/fractalfract9010037Numerical Algorithm for Coupled Fixed Points in Normed Spaces with Applications to Fractional Differential Equations and EconomicsLifang Guo0Salha Alshaikey1Abeer Alshejari2Muhammad Din3Umar Ishtiaq4School of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou 404020, ChinaMathematics Department, Al-Qunfudah University College, Umm Al-Qura University, Mecca 21421, Saudi ArabiaDepartment of Mathematical Sciences, College of Science, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi ArabiaDepartment of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University Rangsit Center, Pathum Thani 12120, ThailandOffice of Research, Innovation and Commercialization, University of Management and Technology, Lahore 54770, PakistanThis paper introduces interpolative enriched cyclic Reich–Rus–Ćirić operators in normed spaces, expanding existing contraction principles by integrating interpolation and cyclic conditions. This class of operators addresses mappings with discontinuities or non-self mappings, enhancing the applicability of fixed-point theory to more complex problems. This class of operators expands on existing cyclic contractions, including interpolative Kannan mappings, interpolative Reich–Rus–Ćirić contractions, and other known contractions in the literature. We demonstrate the existence and uniqueness of fixed points for these operators and provide an example to illustrate our findings. Moreover, we discuss the applications of our results in solving nonlinear integral equations. Furthermore, we introduce the idea of a coupled interpolative enriched cyclic Reich–Rus–Ćirić operator and establish the existence of a strongly coupled fixed-point theorem for this contraction. Finally, we provide an application to fractional differential equations to show the validity of the main result.https://www.mdpi.com/2504-3110/9/1/37enriched contractioncyclic contractioninterpolationReich–Rus–Ćirić contractionfixed pointintegral equation |
| spellingShingle | Lifang Guo Salha Alshaikey Abeer Alshejari Muhammad Din Umar Ishtiaq Numerical Algorithm for Coupled Fixed Points in Normed Spaces with Applications to Fractional Differential Equations and Economics Fractal and Fractional enriched contraction cyclic contraction interpolation Reich–Rus–Ćirić contraction fixed point integral equation |
| title | Numerical Algorithm for Coupled Fixed Points in Normed Spaces with Applications to Fractional Differential Equations and Economics |
| title_full | Numerical Algorithm for Coupled Fixed Points in Normed Spaces with Applications to Fractional Differential Equations and Economics |
| title_fullStr | Numerical Algorithm for Coupled Fixed Points in Normed Spaces with Applications to Fractional Differential Equations and Economics |
| title_full_unstemmed | Numerical Algorithm for Coupled Fixed Points in Normed Spaces with Applications to Fractional Differential Equations and Economics |
| title_short | Numerical Algorithm for Coupled Fixed Points in Normed Spaces with Applications to Fractional Differential Equations and Economics |
| title_sort | numerical algorithm for coupled fixed points in normed spaces with applications to fractional differential equations and economics |
| topic | enriched contraction cyclic contraction interpolation Reich–Rus–Ćirić contraction fixed point integral equation |
| url | https://www.mdpi.com/2504-3110/9/1/37 |
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