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3 results

  • MAPPING PROPERTIES OF A SCALE INVARIANT CASSINIAN METRIC AND A GROMOV HYPERBOLIC METRIC

  • Part of
  • MANAS RANJAN MOHAPATRA, SWADESH KUMAR SAHOO
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 97 / Issue 1 / February 2018
    Published online by Cambridge University Press:
    18 August 2017, pp. 141-152
    Print publication:
    February 2018
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  • We consider a scale invariant Cassinian metric and a Gromov hyperbolic metric. We discuss a distortion property of the scale invariant Cassinian metric under Möbius maps of a punctured ball onto another punctured ball. We obtain a modulus of continuity of the identity map from a domain equipped with the scale invariant Cassinian metric (or the Gromov hyperbolic metric) onto the same domain equipped with the Euclidean metric. Finally, we establish the quasi-invariance properties of both metrics under quasiconformal maps.

  • WEIGHTED PSEUDO-ALMOST PERIODIC SOLUTIONS FOR SOME ABSTRACT DIFFERENTIAL EQUATIONS WITH UNIFORM CONTINUITY

  • Part of
  • LI-LI ZHANG, HONG-XU LI
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 82 / Issue 3 / December 2010
    Published online by Cambridge University Press:
    13 October 2010, pp. 424-436
    Print publication:
    December 2010
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  • In this work, we give some theorems on (mild) weighted pseudo-almost periodic solutions for some abstract semilinear differential equations with uniform continuity. To facilitate this we give a new composition theorem of weighted pseudo-almost periodic functions. Our composition theorem improves the known one by making use of a uniform continuity condition instead of the Lipschitz condition.

  • Uniformly Continuous Partitions of Unity on a Metric Space

  • Stewart M. Robinson, Zachary Robinson
  • Journal:
    Canadian Mathematical Bulletin / Volume 26 / Issue 1 / 01 March 1983
    Published online by Cambridge University Press:
    20 November 2018, pp. 115-117
    Print publication:
    01 March 1983
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  • In this paper, we construct, for any open cover of a metric space, a partition of unity consisting of a family of uniformly continuous functions.