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Zbl 1031.49016
Noor, Muhammad Aslam
Generalized set-valued variational inclusions and resolvent equations.
(English)
[J] J. Math. Anal. Appl. 228, No.1, 206-220 (1998). ISSN 0022-247X

Summary: In this paper, we establish the equivalence between generalized set-valued variational inclusions, resolvent equations, and the fixed-point problem, using the resolvent operator technique. This equivalence is used to suggest and analyze some iterative algorithms for solving generalized set-valued variational inclusions and related optimization problems.
MSC 2000:
*49J40 Variational methods including variational inequalities
49J53 Set-valued and variational analysis
47J20 Inequalities involving nonlinear operators
47H04 Set-valued operators
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces

Keywords: set-valued variational inclusions; resolvent equations; fixed-point problem; resolvent operator technique

Cited in: Zbl 1056.47053 Zbl 1047.49008 Zbl 1070.49006 Zbl 1031.49018 Zbl 1031.49017

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Scientific prize winners of the ICM 2010
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Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

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