منابع مشابه
Metric trees of generalized roundness one
Every finite metric tree has generalized roundness strictly greater than one. On the other hand, some countable metric trees have generalized roundness precisely one. The purpose of this paper is to identify several large classes of countable metric trees that have generalized roundness precisely one. At the outset we consider spherically symmetric trees endowed with the usual path metric (SSTs...
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We present a formal definition of routing metrics and provide the necessary and sufficient conditions for a routing metric to be optimizable along a tree. Based upon these conditions we present a generalization of the shortest path tree which we call the “maximal metric tree”. We present a stabilizing protocol for constructing maximal metric trees. Our protocol demonstrates that the distance-ve...
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The well-known Banach’s fixed point theorem asserts that ifD X, f is contractive and X, d is complete, then f has a unique fixed point inX. It is well known that the Banach contraction principle 1 is a very useful and classical tool in nonlinear analysis. In 1969, Boyd and Wong 2 introduced the notion ofΦ-contraction. A mapping f : X → X on a metric space is called Φ-contraction if there exists...
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ژورنال
عنوان ژورنال: Aequationes mathematicae
سال: 2011
ISSN: 0001-9054,1420-8903
DOI: 10.1007/s00010-011-0108-8