Generalized Yosida Approximations Based on Relatively A-Maximal m-Relaxed Monotonicity Frameworks
We introduce and study a new notion of relatively A-maximal m-relaxed monotonicity framework and discuss some properties of a new class of generalized relatively resolvent operator associated with the relatively A-maximal m-relaxed monotone operator and the new generalized Yosida approximations base...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/157190 |
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| _version_ | 1832567180562006016 |
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| author | Heng-you Lan |
| author_facet | Heng-you Lan |
| author_sort | Heng-you Lan |
| collection | DOAJ |
| description | We introduce and study a new notion of relatively A-maximal m-relaxed monotonicity framework and discuss some properties of a new class of generalized relatively resolvent operator associated with the relatively A-maximal m-relaxed monotone operator and the new generalized Yosida approximations based on relatively A-maximal m-relaxed monotonicity framework. Furthermore, we give some remarks to show that the theory of the new generalized relatively resolvent operator and Yosida approximations associated with relatively A-maximal m-relaxed monotone operators generalizes most of the existing notions on (relatively) maximal monotone mappings in Hilbert as well as Banach space and can be applied to study variational inclusion problems and first-order evolution equations as well as evolution inclusions. |
| format | Article |
| id | doaj-art-8785697a97074b3a978a8899c9c03dad |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-8785697a97074b3a978a8899c9c03dad2025-02-03T01:02:07ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/157190157190Generalized Yosida Approximations Based on Relatively A-Maximal m-Relaxed Monotonicity FrameworksHeng-you Lan0Department of Mathematics, Sichuan University of Science & Engineering, Zigong, Sichuan 643000, ChinaWe introduce and study a new notion of relatively A-maximal m-relaxed monotonicity framework and discuss some properties of a new class of generalized relatively resolvent operator associated with the relatively A-maximal m-relaxed monotone operator and the new generalized Yosida approximations based on relatively A-maximal m-relaxed monotonicity framework. Furthermore, we give some remarks to show that the theory of the new generalized relatively resolvent operator and Yosida approximations associated with relatively A-maximal m-relaxed monotone operators generalizes most of the existing notions on (relatively) maximal monotone mappings in Hilbert as well as Banach space and can be applied to study variational inclusion problems and first-order evolution equations as well as evolution inclusions.http://dx.doi.org/10.1155/2013/157190 |
| spellingShingle | Heng-you Lan Generalized Yosida Approximations Based on Relatively A-Maximal m-Relaxed Monotonicity Frameworks Abstract and Applied Analysis |
| title | Generalized Yosida Approximations Based on Relatively A-Maximal m-Relaxed Monotonicity Frameworks |
| title_full | Generalized Yosida Approximations Based on Relatively A-Maximal m-Relaxed Monotonicity Frameworks |
| title_fullStr | Generalized Yosida Approximations Based on Relatively A-Maximal m-Relaxed Monotonicity Frameworks |
| title_full_unstemmed | Generalized Yosida Approximations Based on Relatively A-Maximal m-Relaxed Monotonicity Frameworks |
| title_short | Generalized Yosida Approximations Based on Relatively A-Maximal m-Relaxed Monotonicity Frameworks |
| title_sort | generalized yosida approximations based on relatively a maximal m relaxed monotonicity frameworks |
| url | http://dx.doi.org/10.1155/2013/157190 |
| work_keys_str_mv | AT hengyoulan generalizedyosidaapproximationsbasedonrelativelyamaximalmrelaxedmonotonicityframeworks |