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2 results

  • CONVERGENCE OF MANN’S ALTERNATING PROJECTIONS IN CAT($\unicode[STIX]{x1D705}$) SPACES

  • Part of
  • BYOUNG JIN CHOI
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 98 / Issue 1 / August 2018
    Published online by Cambridge University Press:
    03 May 2018, pp. 134-143
    Print publication:
    August 2018
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  • We study the convex feasibility problem in $\text{CAT}(\unicode[STIX]{x1D705})$ spaces using Mann’s iterative projection method. To do this, we extend Mann’s projection method in normed spaces to $\text{CAT}(\unicode[STIX]{x1D705})$ spaces with $\unicode[STIX]{x1D705}\geq 0$, and then we prove the $\unicode[STIX]{x1D6E5}$-convergence of the method. Furthermore, under certain regularity or compactness conditions on the convex closed sets, we prove the strong convergence of Mann’s alternating projection sequence in $\text{CAT}(\unicode[STIX]{x1D705})$ spaces with $\unicode[STIX]{x1D705}\geq 0$.

  • EQUI-ATTRACTION AND THE CONTINUOUS DEPENDENCE OF ATTRACTORS ON PARAMETERS

  • LI DESHENG, P. E. KLOEDEN
  • Journal:
    Glasgow Mathematical Journal / Volume 46 / Issue 1 / January 2004
    Published online by Cambridge University Press:
    15 January 2004, pp. 131-141
    Print publication:
    January 2004
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  • The equi-attraction properties concerning the global attractors $\a_\lam$ of dynamical systems $S_\lam(t)$ with parameter $\lam\in\Lam$, where $\Lam$ is a compact metric space, are investigated. In particular, under appropriate conditions, it is shown that the equi-attraction of the family $\{\a_\lam\}$ is equivalent to the continuity of $\a_\lam$ in $\lam$ with respect to the Hausdorff distance.