Equicontinuity, Affine Mean Ergodic Theorem and Linear Equations in Random Normed Spaces

A Mean Ergodic Theorem For Asymptotically Quasi-Nonexpansive Affine Mappings in Banach Spaces Satisfying Opial's Condition

a mean ergodic theorem for asymptotically quasi-nonexpansive affine mappings in banach spaces satisfying opial's condition

Remotality and proximinality in normed linear spaces

In this paper, we consider the concepts farthest points and nearest points in normed linear spaces, We obtain a necessary and coecient conditions for proximinal, Chebyshev, remotal and uniquely remotal subsets in normed linear spaces. Also, we consider -remotality, -proximinality, coproximinality and co-remotality.

a mean ergodic theorem for asymptotically quasi-nonexpansive affine mappings in banach spaces satisfying opial's condition

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A quantitative Mean Ergodic Theorem for uniformly convex Banach spaces

We provide an explicit uniform bound on the local stability of ergodic averages in uniformly convex Banach spaces. Our result can also be viewed as a finitary version in the sense of T. Tao of the Mean Ergodic Theorem for such spaces and so generalizes similar results obtained for Hilbert spaces by Avigad, Gerhardy and Towsner [1] and T. Tao [11].