A system of nonlinear set valued variational inclusions

In this paper, we studied the existence theorems and techniques for finding the solutions of a system of nonlinear set valued variational inclusions in Hilbert spaces. To overcome the difficulties, due to the presence of a proper convex lower semicontinuous function ϕ and a mapping g which appeared...

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Bibliographic Details
Published inSpringerPlus Vol. 3; no. 1; pp. 318 - 10
Main Authors Tang, Yong-Kun, Chang, Shih-sen, Salahuddin, Salahuddin
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 25.06.2014
Springer Nature B.V
BioMed Central Ltd
Subjects
Algorithms
Applied Mathematics
Humanities and Social Sciences
multidisciplinary
Science
Science (multidisciplinary)
Hilbert spaces
Resolvent operators
System of nonlinear set valued variational inclusions
Iterative sequences
Lipschitz continuity
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Summary:In this paper, we studied the existence theorems and techniques for finding the solutions of a system of nonlinear set valued variational inclusions in Hilbert spaces. To overcome the difficulties, due to the presence of a proper convex lower semicontinuous function ϕ and a mapping g which appeared in the considered problems, we have used the resolvent operator technique to suggest an iterative algorithm to compute approximate solutions of the system of nonlinear set valued variational inclusions. The convergence of the iterative sequences generated by algorithm is also proved. AMS Mathematics subject classification 49J40; 47H06
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ISSN:2193-1801
2193-1801
DOI:10.1186/2193-1801-3-318