Generalized set-valued variational-like inclusions and Wiener-Hopf equations in Banach spaces
By using the notion of Jη-proximal mapping for a nonconvex, lower semicontinuous, η-subdifferentiable proper functional in reflexive Banach spaces, we introduce and study a class of generalized set-valued variational-like inclusions in Banach spaces and show their equivalences with a class of Wiener...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2005-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS.2005.3645 |
| Summary: | By using the notion of Jη-proximal mapping for a nonconvex, lower semicontinuous, η-subdifferentiable proper functional in reflexive Banach spaces, we introduce and study a class of generalized set-valued variational-like inclusions in Banach spaces and show their equivalences with a class of Wiener-Hopf equations. We propose two new iterative algorithms for the class of generalized set-valued variational-like inclusions. Furthermore, we prove the existence of solutions of the generalized set-valued variational-like inclusions and the convergence criteria of the two iterative algorithms for the generalized set-valued variational-like inclusions in reflexive Banach spaces. The results presented in this paper are new and are an extension of the corresponding results in this direction. |
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| ISSN: | 0161-1712 1687-0425 |