Strong convergence for a modified forward-backward splitting method in Banach spaces. (English) Zbl 1479.47068
Summary: We propose a modified forward-backward splitting method and prove a new strong convergence theorem of solutions to a zero problem of the sum of a monotone operator and an inverse-strongly-monotone operator in a real 2-uniformly convex and uniformly smooth Banach space. Some new results for variational inequality problems and monotone inclusions are obtained.
MSC:
| 47J25 | Iterative procedures involving nonlinear operators |
| 47H05 | Monotone operators and generalizations |
| 47J22 | Variational and other types of inclusions |
| 49J40 | Variational inequalities |
Keywords:
sum of maximal monotone operators; forward-backward splitting method; variational inequality; inverse strongly monotone operators, 2-uniformly convex Banach space; strong convergenceReferences:
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