The \(p\)-step iterative algorithm for a system of generalized mixed quasi-variational inclusions with \((A,\eta )\)-accretive operators in \(q\)-uniformly smooth Banach spaces. (English) Zbl 1157.65038
A new system of generalized mixed quasi-variational inclusions with \((A,\eta)\)-accretive operators in \(q\)-unifomly smooth Banach spaces, is introduced and studied. A new iterative algorithm is constructed for solving this system of generalized mixed quasi-variational inclusions in real \(q\)-uniformly smooth Banach spaces. Existence and convergence of the solutions are also proved. The results of the paper extend and improve some known results. The techniques involved in the paper will inspire and motivate to introduce and develop new mathematical models in other (related) cases of interests.
Reviewer: Akrur Behera (Rourkela)
MSC:
| 65K10 | Numerical optimization and variational techniques |
| 49J40 | Variational inequalities |
| 49J27 | Existence theories for problems in abstract spaces |
| 49M15 | Newton-type methods |
Keywords:
\(q\)-unifomly smooth Banach spaces; system of generalized mixed quasi-variational inclusions; (\(A, \eta \))-accretive operator; resolvent operator technique; \(p\)-step iterative algorithm; convergenceReferences:
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