Equivalence between resolvent consistency and convergence for nonlinear quasi-contractive algorithms
Simeon Reich · 1979
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 .. 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...