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| Volume 8, Number 1, April 2007, pp. 1-10 | ||||||||
| Dan Butnariu and Elena Resmerita | ||||||||
| Key words: | ||||||||
| Bregman distance, Legendre function, modulus of total convexity, Mosco convergence of a sequence of functions, proximal mapping relative to a convex function, relative projection onto a convex set, uniformly convex function. | ||||||||
| Mathematices Subject Classification: Primary 52A41, 90C48; Secondary 49K40, 90C31. | ||||||||
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| Abstract: | |||
| In this paper we establish criteria for the stability of the proximal mapping Prox f φ= (∂φ + ∂f )-1 associated to the proper lower semicontinuous convex functions φ and f on a reflexive Banach space X. We prove that, under certain conditions, if the convex functions φn converge in the sense of Mosco to φ and if ξn converges strongly to ξ then Prox fφn( ξn ) converges weakly and, if f is also totally convex, then it converges strongly to Proxf φ(ξ). | |||
| Mosco stability of proximal mappings in reflexive Banach spaces | ||