General nonlinear random equations with random multivalued operator in Banach spaces. (English) Zbl 1181.47063
Following H.-Y.Lan, Q.-K.Liu and J.Li [“Iterative approximation for a system of nonlinear variational inclusions involving generalized \(m\)-accretive mappings”, Nonlinear Anal.Forum 9, No.1, 33–42 (2004; Zbl 1064.49006)], R.Ahmad and F.F.Bazán [“An iterative algorithm for random generalized nonlinear mixed variational inclusions for random fuzzy mappings”, Appl.Math.Comput.167, No.2, 1400–1411 (2005; Zbl 1081.65060)] and R.U.Verma [“A class of projection-contraction methods applied to monotone variational inequalities”, Appl.Math.Lett.13, No.8, 55–62 (2000; Zbl 0988.47041)], the authors study a new class of random multivalued nonlinear operator equations involving generalized \(m\)-accretive mappings in Banach spaces. Further, they obtain existence and convergence theorems for random multivalued operator equations in \(q\)-uniformly smooth Banach spaces. Some special cases are also discussed.
Reviewer: S. L. Singh (Rishikesh)
MSC:
| 47H40 | Random nonlinear operators |
| 47H10 | Fixed-point theorems |
| 47H06 | Nonlinear accretive operators, dissipative operators, etc. |
| 47J25 | Iterative procedures involving nonlinear operators |
| 54H25 | Fixed-point and coincidence theorems (topological aspects) |
Keywords:
random operator; random multivalued operator; strongly accretive operator; Lipschitz continuous; \(m\)-accretive operatorReferences:
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