Research on Adjoint Kernelled Quasidifferential
The quasidifferential of a quasidifferentiable function in the sense of Demyanov and Rubinov is not uniquely defined. Xia proposed the notion of the kernelled quasidifferential, which is expected to be a representative for the equivalence class of quasidifferentials. Although the kernelled quasidiff...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/131482 |
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| author | Si-Da Lin Fu-Min Xiao Zun-Quan Xia Li-Ping Pang |
| author_facet | Si-Da Lin Fu-Min Xiao Zun-Quan Xia Li-Ping Pang |
| author_sort | Si-Da Lin |
| collection | DOAJ |
| description | The quasidifferential of a quasidifferentiable function in the sense of Demyanov and Rubinov is not uniquely defined. Xia proposed the notion of the kernelled quasidifferential, which is expected to be a representative for the equivalence class of quasidifferentials. Although the kernelled quasidifferential is known to have good algebraic properties and geometric structure, it is still not very convenient for calculating the kernelled quasidifferentials of −f and minfi∣i∈a finite index set I, where f and fi are kernelled quasidifferentiable functions. In this paper, the notion of adjoint kernelled quasidifferential, which is well-defined for −f and minfi∣i∈I, is employed as a representative of the equivalence class of quasidifferentials. Some algebraic properties of the adjoint kernelled quasidifferential are given and the existence of the adjoint kernelled quasidifferential is explored by means of the minimal quasidifferential and the Demyanov difference of convex sets. Under some condition, a formula of the adjoint kernelled quasidifferential is presented. |
| format | Article |
| id | doaj-art-ccb81fa266cc42818536e4ab7b173ea9 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-ccb81fa266cc42818536e4ab7b173ea92025-02-03T01:24:22ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/131482131482Research on Adjoint Kernelled QuasidifferentialSi-Da Lin0Fu-Min Xiao1Zun-Quan Xia2Li-Ping Pang3School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, ChinaDepartment of Hydrography & Cartography, PLA Dalian Naval Academy, Dalian 116018, ChinaSchool of Mathematical Sciences, Dalian University of Technology, Dalian 116024, ChinaSchool of Mathematical Sciences, Dalian University of Technology, Dalian 116024, ChinaThe quasidifferential of a quasidifferentiable function in the sense of Demyanov and Rubinov is not uniquely defined. Xia proposed the notion of the kernelled quasidifferential, which is expected to be a representative for the equivalence class of quasidifferentials. Although the kernelled quasidifferential is known to have good algebraic properties and geometric structure, it is still not very convenient for calculating the kernelled quasidifferentials of −f and minfi∣i∈a finite index set I, where f and fi are kernelled quasidifferentiable functions. In this paper, the notion of adjoint kernelled quasidifferential, which is well-defined for −f and minfi∣i∈I, is employed as a representative of the equivalence class of quasidifferentials. Some algebraic properties of the adjoint kernelled quasidifferential are given and the existence of the adjoint kernelled quasidifferential is explored by means of the minimal quasidifferential and the Demyanov difference of convex sets. Under some condition, a formula of the adjoint kernelled quasidifferential is presented.http://dx.doi.org/10.1155/2014/131482 |
| spellingShingle | Si-Da Lin Fu-Min Xiao Zun-Quan Xia Li-Ping Pang Research on Adjoint Kernelled Quasidifferential Abstract and Applied Analysis |
| title | Research on Adjoint Kernelled Quasidifferential |
| title_full | Research on Adjoint Kernelled Quasidifferential |
| title_fullStr | Research on Adjoint Kernelled Quasidifferential |
| title_full_unstemmed | Research on Adjoint Kernelled Quasidifferential |
| title_short | Research on Adjoint Kernelled Quasidifferential |
| title_sort | research on adjoint kernelled quasidifferential |
| url | http://dx.doi.org/10.1155/2014/131482 |
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