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Search: All articles in the CMB digital archive with keyword hyperbolic metric

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1. CMB Online first

Khamsi, M. A.
Approximate Fixed Point Sequences of Nonlinear Semigroup in Metric Spaces
In this paper, we investigate the common approximate fixed point sequences of nonexpansive semigroups of nonlinear mappings $\{T_t\}_{t \geq 0}$, i.e., a family such that $T_0(x)=x$, $T_{s+t}=T_s(T_t(x))$, where the domain is a metric space $(M,d)$. In particular we prove that under suitable conditions, the common approximate fixed point sequences set is the same as the common approximate fixed point sequences set of two mappings from the family. Then we use the Ishikawa iteration to construct a common approximate fixed point sequence of nonexpansive semigroups of nonlinear mappings.

Keywords:approximate fixed point, fixed point, hyperbolic metric space, Ishikawa iterations, nonexpansive mapping, semigroup of mappings, uniformly convex hyperbolic space
Categories:47H09, 46B20, 47H10, 47E10

2. CMB 2012 (vol 56 pp. 241)

Betsakos, Dimitrios; Pouliasis, Stamatis
Versions of Schwarz's Lemma for Condenser Capacity and Inner Radius
We prove variants of Schwarz's lemma involving monotonicity properties of condenser capacity and inner radius. Also, we examine when a similar monotonicity property holds for the hyperbolic metric.

Keywords:condenser capacity, inner radius, hyperbolic metric, Schwarz's lemma
Categories:30C80, 30F45, 31A15

3. CMB 2009 (vol 52 pp. 613)

Wulan, Hasi; Zhu, Kehe
Lipschitz Type Characterizations for Bergman Spaces
We obtain new characterizations for Bergman spaces with standard weights in terms of Lipschitz type conditions in the Euclidean, hyperbolic, and pseudo-hyperbolic metrics. As a consequence, we prove optimal embedding theorems when an analytic function on the unit disk is symmetrically lifted to the bidisk.

Keywords:Bergman spaces, hyperbolic metric, Lipschitz condition

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