A New Intrinsic Metric on Metric Spaces
A new intrinsic metric called S D -metric is introduced for a general metric space ( X , d ), where D is a non-trivial bounded closed subset of X . The metric S D can be used to define a strongly hyperbolic metric on X . We consider the convergence of metric spaces { ( X , S D n ) } n = 1 ∞ for a s...
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| Veröffentlicht in: | Bulletin of the Malaysian Mathematical Sciences Society 2022-11, Vol.45 (6), p.2941-2958 |
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| container_title | Bulletin of the Malaysian Mathematical Sciences Society |
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| creator | Cui, Yumiao Xiao, Yingqing |
| description | A new intrinsic metric called
S
D
-metric is introduced for a general metric space (
X
,
d
), where
D
is a non-trivial bounded closed subset of
X
. The metric
S
D
can be used to define a strongly hyperbolic metric on
X
. We consider the convergence of metric spaces
{
(
X
,
S
D
n
)
}
n
=
1
∞
for a sequence of non-trivial bounded closed subsets
{
D
n
}
n
=
1
∞
. The distortion property of the new metric on the unit ball
B
n
is also studied under the Möbius transformations of the unit ball. |
| doi_str_mv | 10.1007/s40840-022-01310-3 |
| format | Article |
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S
D
-metric is introduced for a general metric space (
X
,
d
), where
D
is a non-trivial bounded closed subset of
X
. The metric
S
D
can be used to define a strongly hyperbolic metric on
X
. We consider the convergence of metric spaces
{
(
X
,
S
D
n
)
}
n
=
1
∞
for a sequence of non-trivial bounded closed subsets
{
D
n
}
n
=
1
∞
. The distortion property of the new metric on the unit ball
B
n
is also studied under the Möbius transformations of the unit ball.</description><identifier>ISSN: 0126-6705</identifier><identifier>EISSN: 2180-4206</identifier><identifier>DOI: 10.1007/s40840-022-01310-3</identifier><language>eng</language><publisher>Singapore: Springer Nature Singapore</publisher><subject>Applications of Mathematics ; Geometric transformation ; Mathematics ; Mathematics and Statistics ; Metric space</subject><ispartof>Bulletin of the Malaysian Mathematical Sciences Society, 2022-11, Vol.45 (6), p.2941-2958</ispartof><rights>The Author(s), under exclusive licence to Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2022</rights><rights>The Author(s), under exclusive licence to Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2022.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c200t-ff5c00578aef98e5414574743c9c71aa76063f71059a7f8225d6ff1b16e5ca753</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s40840-022-01310-3$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s40840-022-01310-3$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27903,27904,41467,42536,51298</link.rule.ids></links><search><creatorcontrib>Cui, Yumiao</creatorcontrib><creatorcontrib>Xiao, Yingqing</creatorcontrib><title>A New Intrinsic Metric on Metric Spaces</title><title>Bulletin of the Malaysian Mathematical Sciences Society</title><addtitle>Bull. Malays. Math. Sci. Soc</addtitle><description>A new intrinsic metric called
S
D
-metric is introduced for a general metric space (
X
,
d
), where
D
is a non-trivial bounded closed subset of
X
. The metric
S
D
can be used to define a strongly hyperbolic metric on
X
. We consider the convergence of metric spaces
{
(
X
,
S
D
n
)
}
n
=
1
∞
for a sequence of non-trivial bounded closed subsets
{
D
n
}
n
=
1
∞
. The distortion property of the new metric on the unit ball
B
n
is also studied under the Möbius transformations of the unit ball.</description><subject>Applications of Mathematics</subject><subject>Geometric transformation</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Metric space</subject><issn>0126-6705</issn><issn>2180-4206</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><recordid>eNp9kE9LAzEQxYMoWGq_gKcFD56iM5N_u8dS1BaqHtRziDGRFt1dky3itze6ijfn8t7hvTfwY-wY4QwBzHmWUEvgQMQBBQIXe2xCWAOXBHqfTQBJc21AHbJZzlsopzRpwgk7nVc34b1atUPatHnjq-tQnK-69tfd9c6HfMQOonvJYfajU_ZweXG_WPL17dVqMV9zTwADj1H5Mm5qF2JTByVRKiONFL7xBp0zGrSIBkE1zsSaSD3pGPERdVDeGSWm7GTc7VP3tgt5sNtul9ry0pKhppHQSCwpGlM-dTmnEG2fNq8ufVgE-8XEjkxsYWK_mVhRSmIs5RJun0P6m_6n9QnZXWB9</recordid><startdate>20221101</startdate><enddate>20221101</enddate><creator>Cui, Yumiao</creator><creator>Xiao, Yingqing</creator><general>Springer Nature Singapore</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20221101</creationdate><title>A New Intrinsic Metric on Metric Spaces</title><author>Cui, Yumiao ; Xiao, Yingqing</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c200t-ff5c00578aef98e5414574743c9c71aa76063f71059a7f8225d6ff1b16e5ca753</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Applications of Mathematics</topic><topic>Geometric transformation</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Metric space</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Cui, Yumiao</creatorcontrib><creatorcontrib>Xiao, Yingqing</creatorcontrib><collection>CrossRef</collection><jtitle>Bulletin of the Malaysian Mathematical Sciences Society</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Cui, Yumiao</au><au>Xiao, Yingqing</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A New Intrinsic Metric on Metric Spaces</atitle><jtitle>Bulletin of the Malaysian Mathematical Sciences Society</jtitle><stitle>Bull. Malays. Math. Sci. Soc</stitle><date>2022-11-01</date><risdate>2022</risdate><volume>45</volume><issue>6</issue><spage>2941</spage><epage>2958</epage><pages>2941-2958</pages><issn>0126-6705</issn><eissn>2180-4206</eissn><abstract>A new intrinsic metric called
S
D
-metric is introduced for a general metric space (
X
,
d
), where
D
is a non-trivial bounded closed subset of
X
. The metric
S
D
can be used to define a strongly hyperbolic metric on
X
. We consider the convergence of metric spaces
{
(
X
,
S
D
n
)
}
n
=
1
∞
for a sequence of non-trivial bounded closed subsets
{
D
n
}
n
=
1
∞
. The distortion property of the new metric on the unit ball
B
n
is also studied under the Möbius transformations of the unit ball.</abstract><cop>Singapore</cop><pub>Springer Nature Singapore</pub><doi>10.1007/s40840-022-01310-3</doi><tpages>18</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0126-6705 |
| ispartof | Bulletin of the Malaysian Mathematical Sciences Society, 2022-11, Vol.45 (6), p.2941-2958 |
| issn | 0126-6705 2180-4206 |
| language | eng |
| recordid | cdi_proquest_journals_2729940941 |
| source | Springer Nature - Complete Springer Journals |
| subjects | Applications of Mathematics Geometric transformation Mathematics Mathematics and Statistics Metric space |
| title | A New Intrinsic Metric on Metric Spaces |
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