• 제목/요약/키워드: nonlinear semigroups

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DISKCYCLIC C0-SEMIGROUPS AND DISKCYCLICITY CRITERIA

  • Moosapoor, Mansooreh
    • Nonlinear Functional Analysis and Applications
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    • 제27권1호
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    • pp.111-119
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    • 2022

  • In this article, we prove that diskcyclic C0-semigroups exist on any infinite-dimensional Banach space. We show that a C0-semigroup (Tt)t≥0 satisfies the diskcyclicity criterion if and only if any of Tt's satisfies the diskcyclicity criterion for operators. Moreover, we show that there are diskcyclic C0-semigroups that do not satisfy the diskcyclicity criterion. Also, we state various criteria for diskcyclicity of C0-semigroups based on dense sets and d-dense orbits.

  • https://doi.org/10.22771/nfaa.2022.27.01.07 인용 PDF KSCI

NONLINEAR SEMIGROUPS AND DIFFERENTIAL INCLUSIONS IN PROBABILISTIC NORMED SPACES

  • Chang, S.S.;Ha, K.S.;Cho, Y.J.;Lee, B.S.;Chen, Y.Q.
    • East Asian mathematical journal
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    • 제14권1호
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    • pp.77-98
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    • 1998

  • The purpose of this paper is to introduce and study the semigroups of nonlinear contractions in probabilistic normed spaces and to establish the Crandall-Liggett's exponential formula for some kind of accretive mappings in probabilistic normed spaces. As applications, we utilize these results to study the Cauchy problem for a kind of differential inclusions with accertive mappings in probabilistic normed spaces.

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ON THE STRONG CONVERGENCE THEOREMS FOR ASYMPTOTICALLY NONEXPANSIVE SEMIGROUPS IN BANACH SPACES

  • Chang, Shih-Sen;Zhao, Liang Cai;Wu, Ding Ping
    • Journal of applied mathematics & informatics
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    • 제27권1_2호
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    • pp.13-23
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    • 2009

  • Some strong convergence theorems of explicit iteration scheme for asymptotically nonexpansive semi-groups in Banach spaces are established. The results presented in this paper extend and improve some recent results in [T. Suzuki. On strong convergence to common fixed points of nonexpansive semigroups in Hilbert spaces, Proc. Amer. Math. Soc. 131(2002)2133-2136; H. K. Xu. A strong convergence theorem for contraction semigroups in Banach spaces, Bull. Aust. Math. Soc. 72(2005)371-379; N. Shioji and W. Takahashi. Strong convergence theorems for continuous semigroups in Banach spaces, Math. Japonica. 1(1999)57-66; T. Shimizu and W. Takahashi. Strong convergence to common fixed points of families of nonexpansive mappings, J. Math. Anal. Appl. 211(1997)71-83; N. Shioji and W. Takahashi. Strong convergence theorems for asymptotically nonexpansive mappings in Hilbert spaces, Nonlinear Anal. TMA, 34(1998)87-99; H. K. Xu. Approximations to fixed points of contraction semigroups in Hilbert space, Numer. Funct. Anal. Optim. 19(1998), 157-163.]

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