Naoki Shioji
Yokohama National University
51 Papers
450 Citations
Naoki Shioji is an academic researcher from Yokohama National University. The author has contributed to research in topics: Banach space & Nonlinear system. The author has an hindex of 17, co-authored 49 publications. Previous affiliations of Naoki Shioji include Tamagawa University & Tokyo Institute of Technology.
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Papers
Existence of Nonexpansive Retractions for Amenable Semigroups of Nonexpansive Mappings and Nonlinear Ergodic Theorems in Banach Spaces
TL;DR: In this paper, the authors studied nonlinear ergodic properties for an amenable semigroup of nonexpansive mappings in a Banach space, and proved that if S = Tt: t∈S} is a nonexPansive semigroup on a closed, convex subsetCin a uniformly convex spaceE such that the setF(S) of common fixed points of S is nonempty, then there exists a nonex-preserving retractionPfromContoF(s) such thatPTt=TtP=Pfor each
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Strong Convergence of Averaged Approximants for Asymptotically Nonexpansive Mappings in Banach Spaces
Naoki Shioji,Wataru Takahashi +1 more
TL;DR: In this article, a closed, convex subset of a uniformly convex Banach space whose norm is uniformly Gâteaux differentiable and an asymptotically nonexpansive mapping from Cinto itself such that the setF(T) of fixed points of T is nonempty is shown to be a sunny, nonexpANSive retract of C.
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COMPACT EMBEDDINGS FOR SOBOLEV SPACES OF VARIABLE EXPONENTS AND EXISTENCE OF SOLUTIONS FOR NONLINEAR ELLIPTIC PROBLEMS INVOLVING THE p(x)-LAPLACIAN AND ITS CRITICAL EXPONENT
TL;DR: In this paper, the authors give a sucient condition for the compact embedding from W k;p(¢) 0 (›) to L q (¢) ( ›) in case L q = 0, where › is a bounded open set in R N.
A strong convergence theorem for asymptotically nonexpansive mappings in Banach spaces
Naoki Shioji,Wataru Takahashi +1 more
TL;DR: In this paper, the convergence of a sequence of real numbers with the norm of Gâteaux differentiable real numbers is studied for the case where n = 0, 1, 2, 3, 4, 5, 6.
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