Fixed Point Theorems of Superlinear Operators with Applications
In this paper, by using the partial order method and monotone iterative techniques, the existence and uniqueness of fixed points for a class of superlinear operators are studied, without requiring any compactness or continuity. As corollaries, the new fixed point theorems for α-convex operators α>...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2022-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2022/2965300 |
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| _version_ | 1832550886802456576 |
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| author | Shaoyuan Xu Yan Han |
| author_facet | Shaoyuan Xu Yan Han |
| author_sort | Shaoyuan Xu |
| collection | DOAJ |
| description | In this paper, by using the partial order method and monotone iterative techniques, the existence and uniqueness of fixed points for a class of superlinear operators are studied, without requiring any compactness or continuity. As corollaries, the new fixed point theorems for α-convex operators α>1, e-convex operators, positive α homogeneous operator α>1, generalized e-convex operator, and convex operators are obtained. The results are applied to nonlinear integral equations and partial differential equations. |
| format | Article |
| id | doaj-art-1ecb487871154fd9879aa66c7d41eada |
| institution | Kabale University |
| issn | 2314-8888 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-1ecb487871154fd9879aa66c7d41eada2025-02-03T06:05:25ZengWileyJournal of Function Spaces2314-88882022-01-01202210.1155/2022/2965300Fixed Point Theorems of Superlinear Operators with ApplicationsShaoyuan Xu0Yan Han1School of Mathematics and StatisticsSchool of Mathematics and StatisticsIn this paper, by using the partial order method and monotone iterative techniques, the existence and uniqueness of fixed points for a class of superlinear operators are studied, without requiring any compactness or continuity. As corollaries, the new fixed point theorems for α-convex operators α>1, e-convex operators, positive α homogeneous operator α>1, generalized e-convex operator, and convex operators are obtained. The results are applied to nonlinear integral equations and partial differential equations.http://dx.doi.org/10.1155/2022/2965300 |
| spellingShingle | Shaoyuan Xu Yan Han Fixed Point Theorems of Superlinear Operators with Applications Journal of Function Spaces |
| title | Fixed Point Theorems of Superlinear Operators with Applications |
| title_full | Fixed Point Theorems of Superlinear Operators with Applications |
| title_fullStr | Fixed Point Theorems of Superlinear Operators with Applications |
| title_full_unstemmed | Fixed Point Theorems of Superlinear Operators with Applications |
| title_short | Fixed Point Theorems of Superlinear Operators with Applications |
| title_sort | fixed point theorems of superlinear operators with applications |
| url | http://dx.doi.org/10.1155/2022/2965300 |
| work_keys_str_mv | AT shaoyuanxu fixedpointtheoremsofsuperlinearoperatorswithapplications AT yanhan fixedpointtheoremsofsuperlinearoperatorswithapplications |