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Ding, Xie Ping; Yao, Jen-Chih

Existence and algorithm of solutions for mixed quasi-variational-like inclusions in Banach spaces. (English) Zbl 1086.46048

Comput. Math. Appl. 49, No. 5-6, 857-869 (2005).
Summary: We study a class of mixed quasi-variational-like inclusions with a bifunction in reflexive Banach spaces. By applying a minimax inequality due to the first author, some existence and uniqueness theorems for solutions of mixed quasi-variational-like inclusions are proved. Next, by applying the auxiliary variational inequality technique, we suggest an iterative algorithm to compute the approximate solutions of mixed quasi-variational-like inclusions. The convergence criteria of the algorithm are studied under quite mild conditions.

Cited in 2 Reviews
Cited in 31 Documents

MSC:

46N10 Applications of functional analysis in optimization, convex analysis, mathematical programming, economics
49J40 Variational inequalities

Keywords:

mixed quasi-variational-like inclusion; minimax inequality; auxiliary variational inequality; iterative algorithm; Banach space
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References:

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