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1. CMB Online first
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 2008 (vol 51 pp. 413)
Big Ramsey Degrees and Divisibility in Classes of Ultrametric Spaces Given a countable set $S$ of positive reals, we study
finite-dimensional Ramsey-theoretic properties of the countable
ultrametric Urysohn space $\textbf{Q} _S$ with distances in $S$.
Keywords:Ramsey theory, Urysohn metric spaces, ultrametric spaces Categories:05C50, 54E35 |
3. CMB 2007 (vol 50 pp. 291)
Beurling's Theorem and Characterization of Heat Kernel for Riemannian Symmetric Spaces of Noncompact Type |
Beurling's Theorem and Characterization of Heat Kernel for Riemannian Symmetric Spaces of Noncompact Type We prove Beurling's theorem for rank $1$ Riemannian symmetric
spaces and relate its consequences with the characterization of
the heat kernel of the symmetric space.
Keywords:Beurling's Theorem, Riemannian symmetric spaces, uncertainty principle Categories:22E30, 43A85 |