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Existence and stability of iterative algorithms for the system of nonlinear quasi-mixed equilibrium problems. (English) Zbl 1220.47125

Let be a real Hilbert space and the maps Φ 1 ,Φ 2 :× satisfy Φ i (x,x)=0, i=1,2; let T 1 ,T 2 :× be nonlinear maps, and C 1 ,C 2 : be multimaps with nonempty convex closed values. The authors consider the problem of finding (x * ,y * )× such that x * C 1 (x * ), y * C 2 (y * ) and

Φ 1 (x * ,z)+(T 1 (x * ,y * ),z-x * )0,zC 1 (x * ),Φ 2 (y * ,z)+(T 2 (x * ,y * ),z-y * )0,zC 2 (y * )·

They prove existence and uniqueness results and describe convergence and stability of a Mann type iterative algorithm.

MSC:
47J25Iterative procedures (nonlinear operator equations)
47J20Inequalities involving nonlinear operators
47H04Set-valued operators
47H05Monotone operators (with respect to duality) and generalizations
47H10Fixed point theorems for nonlinear operators on topological linear spaces
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