Equivalence between resolvent consistency and convergence for nonlinear quasi-contractive algorithms

Technical Report · Fri Jun 01 04:00:00 EDT 1979

DOI:https://doi.org/10.2172/5922508· OSTI ID:5922508

Reich, S.

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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