Equivalence between resolvent consistency and convergence for nonlinear quasi-contractive algorithms
Let E be a reflexive Banach space with a uniformly Gateaux differentiable norm; D, a closed convex subset of E; and C, a nonexpansive retract of D. Let F(t): D ..-->.. C, 0 less than or equal to t < infinity, be a continuous family of mappings with F(0) = I on C, such that abs. value (F(t)x-F(t)y) less than or equal to (M(t))(abs. value (x-y)) for x and y in D and t greater than or equal to 0 with M(t) = 1 + ..omega..t + o(t) as t ..-->.. 0+ for some ..omega.. greater than or equal to 0. If lim/sub n ..-->.. infinity/ F(t/n)/sup n/x = S(t)x exists for each x in C uniformly on compact t intervals, then lim/sub t ..-->.. 0+/(I + (lambdat)(I-Ft)))/sup -1/x = J/sub lambda/x exists for each x in D and 0 < lambda < 1/..omega...
- Research Organization:
- Argonne National Laboratory (ANL), Argonne, IL (United States)
- DOE Contract Number:
- W-31109-ENG-38
- OSTI ID:
- 5922508
- Report Number(s):
- ANL-79-53
- Country of Publication:
- United States
- Language:
- English
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