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Nonlinear Ergodic Theorems for Semigroups of Non-Lipschitzian Mappings in Banach Spaces II

Isao Miyadera

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Abstract

Let C be a nonempty closed convex subset of a uniformly convex Banach space, and let S = {T(t); t ≥ 0} be a nonlinear semigroup of non-Lipschitzian mappings on C which is asymptotically nonexpansive in the intermediate sense. In this paper we study weak almost convergence of almost-orbits of S.

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Let C be a nonempty closed convex subset of a uniformly convex Banach space, and let S = {T(t); t ≥ 0} be a nonlinear semigroup of non-Lipschitzian mappings on C which is asymptotically nonexpansive in the intermediate sense. In this paper we study weak almost convergence of almost-orbits of S.

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Available abstract

Let C be a nonempty closed convex subset of a uniformly convex Banach space, and let S = {T(t); t ≥ 0} be a nonlinear semigroup of non-Lipschitzian mappings on C which is asymptotically nonexpansive in the intermediate sense. In this paper we study weak almost convergence of almost-orbits of S.

Key concepts: Mathematics, Banach space, Ergodic theory, Semigroup, Regular polygon, Pure mathematics, Nonlinear system, Uniformly convex space

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