A Cauchy type inequality for Möbius operations

In this article, we show two fundamental features of the restriction of Möbius operations to the real numbers, that is, a Cauchy type inequality and a criterion for convergence of series.

Saved in:
Bibliographic Details
Published in:Journal of inequalities and applications 2018, Vol.2018 (1), p.1-9, Article 97
Main Author: Watanabe, Keiichi
Format: Article
Language:English
Subjects:
Analysis
Applications of Mathematics
Cauchy inequality
Convergence of series
Mathematics
Mathematics and Statistics
Möbius addition
Möbius scalar multiplication
Real numbers
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by cdi_FETCH-LOGICAL-c536t-3330c376b7048251a87a5d1edef840c68ea9d220d0f2ed3bc29eebec73a388433
cites cdi_FETCH-LOGICAL-c536t-3330c376b7048251a87a5d1edef840c68ea9d220d0f2ed3bc29eebec73a388433
container_end_page 9
container_issue 1
container_start_page 1
container_title Journal of inequalities and applications
container_volume 2018
creator Watanabe, Keiichi
description In this article, we show two fundamental features of the restriction of Möbius operations to the real numbers, that is, a Cauchy type inequality and a criterion for convergence of series.
doi_str_mv 10.1186/s13660-018-1690-2
format article
fullrecord <record><control><sourceid>proquest_doaj_</sourceid><recordid>TN_cdi_doaj_primary_oai_doaj_org_article_445b3227d3d94d6d92761b2fe2e87dad</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><doaj_id>oai_doaj_org_article_445b3227d3d94d6d92761b2fe2e87dad</doaj_id><sourcerecordid>2030106497</sourcerecordid><originalsourceid>FETCH-LOGICAL-c536t-3330c376b7048251a87a5d1edef840c68ea9d220d0f2ed3bc29eebec73a388433</originalsourceid><addsrcrecordid>eNp1kc9q3DAQxkVJadK0D5CbIWc3o5GsP5dAWJI2kNJLC70JWRpvvGysjWQH9sXyAnmxOnVom0NPM8x8328YPsZOOHzi3KizwoVSUAM3NVcWanzDjjigrVHiz4N_-kP2vpQNAHJh5Dt2iFYjGNkcsbOLauWncLuvxv2Oqn6g-8lv-3FfdSlXX58e234qVdpR9mOfhvKBve38ttDHl3rMflxdfl99qW--fb5eXdzUoRFqrIUQEIRWrQZpsOHeaN9ETpE6IyEoQ95GRIjQIUXRBrRELQUtvDBGCnHMrhduTH7jdrm_83nvku_d70HKa-fz2IctOSmbViDqKKKVUUWLWvEWO0IyOvo4s84X1m5q7ygGGsbst6-grzdDf-vW6cE1ljcNyhlw-gLI6X6iMrpNmvIw_-8QBHBQ0upZxRdVyKmUTN2fCxzcc15uycvNebnnvBzOHlw8ZdYOa8p_yf83_QLl75bY</addsrcrecordid><sourcetype>Open Website</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2030106497</pqid></control><display><type>article</type><title>A Cauchy type inequality for Möbius operations</title><source>Springer Nature - SpringerLink Journals - Fully Open Access </source><source>Publicly Available Content (ProQuest)</source><creator>Watanabe, Keiichi</creator><creatorcontrib>Watanabe, Keiichi</creatorcontrib><description>In this article, we show two fundamental features of the restriction of Möbius operations to the real numbers, that is, a Cauchy type inequality and a criterion for convergence of series.</description><identifier>ISSN: 1029-242X</identifier><identifier>ISSN: 1025-5834</identifier><identifier>EISSN: 1029-242X</identifier><identifier>DOI: 10.1186/s13660-018-1690-2</identifier><identifier>PMID: 29720845</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Analysis ; Applications of Mathematics ; Cauchy inequality ; Convergence of series ; Mathematics ; Mathematics and Statistics ; Möbius addition ; Möbius scalar multiplication ; Real numbers</subject><ispartof>Journal of inequalities and applications, 2018, Vol.2018 (1), p.1-9, Article 97</ispartof><rights>The Author(s) 2018</rights><rights>Journal of Inequalities and Applications is a copyright of Springer, (2018). All Rights Reserved.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c536t-3330c376b7048251a87a5d1edef840c68ea9d220d0f2ed3bc29eebec73a388433</citedby><cites>FETCH-LOGICAL-c536t-3330c376b7048251a87a5d1edef840c68ea9d220d0f2ed3bc29eebec73a388433</cites><orcidid>0000-0002-6755-7140</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.proquest.com/docview/2030106497/fulltextPDF?pq-origsite=primo$$EPDF$$P50$$Gproquest$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://www.proquest.com/docview/2030106497?pq-origsite=primo$$EHTML$$P50$$Gproquest$$Hfree_for_read</linktohtml><link.rule.ids>230,314,780,784,885,4024,25753,27923,27924,27925,37012,44590,75126</link.rule.ids></links><search><creatorcontrib>Watanabe, Keiichi</creatorcontrib><title>A Cauchy type inequality for Möbius operations</title><title>Journal of inequalities and applications</title><addtitle>J Inequal Appl</addtitle><description>In this article, we show two fundamental features of the restriction of Möbius operations to the real numbers, that is, a Cauchy type inequality and a criterion for convergence of series.</description><subject>Analysis</subject><subject>Applications of Mathematics</subject><subject>Cauchy inequality</subject><subject>Convergence of series</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Möbius addition</subject><subject>Möbius scalar multiplication</subject><subject>Real numbers</subject><issn>1029-242X</issn><issn>1025-5834</issn><issn>1029-242X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><sourceid>PIMPY</sourceid><sourceid>DOA</sourceid><recordid>eNp1kc9q3DAQxkVJadK0D5CbIWc3o5GsP5dAWJI2kNJLC70JWRpvvGysjWQH9sXyAnmxOnVom0NPM8x8328YPsZOOHzi3KizwoVSUAM3NVcWanzDjjigrVHiz4N_-kP2vpQNAHJh5Dt2iFYjGNkcsbOLauWncLuvxv2Oqn6g-8lv-3FfdSlXX58e234qVdpR9mOfhvKBve38ttDHl3rMflxdfl99qW--fb5eXdzUoRFqrIUQEIRWrQZpsOHeaN9ETpE6IyEoQ95GRIjQIUXRBrRELQUtvDBGCnHMrhduTH7jdrm_83nvku_d70HKa-fz2IctOSmbViDqKKKVUUWLWvEWO0IyOvo4s84X1m5q7ygGGsbst6-grzdDf-vW6cE1ljcNyhlw-gLI6X6iMrpNmvIw_-8QBHBQ0upZxRdVyKmUTN2fCxzcc15uycvNebnnvBzOHlw8ZdYOa8p_yf83_QLl75bY</recordid><startdate>2018</startdate><enddate>2018</enddate><creator>Watanabe, Keiichi</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><general>SpringerOpen</general><scope>C6C</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7TB</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>FR3</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>KR7</scope><scope>L6V</scope><scope>M7S</scope><scope>P5Z</scope><scope>P62</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>5PM</scope><scope>DOA</scope><orcidid>https://orcid.org/0000-0002-6755-7140</orcidid></search><sort><creationdate>2018</creationdate><title>A Cauchy type inequality for Möbius operations</title><author>Watanabe, Keiichi</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c536t-3330c376b7048251a87a5d1edef840c68ea9d220d0f2ed3bc29eebec73a388433</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Analysis</topic><topic>Applications of Mathematics</topic><topic>Cauchy inequality</topic><topic>Convergence of series</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Möbius addition</topic><topic>Möbius scalar multiplication</topic><topic>Real numbers</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Watanabe, Keiichi</creatorcontrib><collection>Springer_OA刊</collection><collection>CrossRef</collection><collection>Mechanical &amp; Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science &amp; Engineering Collection</collection><collection>ProQuest Central (Alumni)</collection><collection>ProQuest Central</collection><collection>Advanced Technologies &amp; Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>AUTh Library subscriptions: ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central</collection><collection>Engineering Research Database</collection><collection>ProQuest Central Student</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer Science Database</collection><collection>Civil Engineering Abstracts</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Advanced Technologies &amp; Aerospace Database</collection><collection>ProQuest Advanced Technologies &amp; Aerospace Collection</collection><collection>Publicly Available Content (ProQuest)</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection><collection>PubMed Central (Full Participant titles)</collection><collection>DOAJ Directory of Open Access Journals</collection><jtitle>Journal of inequalities and applications</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Watanabe, Keiichi</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A Cauchy type inequality for Möbius operations</atitle><jtitle>Journal of inequalities and applications</jtitle><stitle>J Inequal Appl</stitle><date>2018</date><risdate>2018</risdate><volume>2018</volume><issue>1</issue><spage>1</spage><epage>9</epage><pages>1-9</pages><artnum>97</artnum><issn>1029-242X</issn><issn>1025-5834</issn><eissn>1029-242X</eissn><abstract>In this article, we show two fundamental features of the restriction of Möbius operations to the real numbers, that is, a Cauchy type inequality and a criterion for convergence of series.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><pmid>29720845</pmid><doi>10.1186/s13660-018-1690-2</doi><tpages>9</tpages><orcidid>https://orcid.org/0000-0002-6755-7140</orcidid><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 1029-242X
ispartof Journal of inequalities and applications, 2018, Vol.2018 (1), p.1-9, Article 97
issn 1029-242X
1025-5834
1029-242X
language eng
recordid cdi_doaj_primary_oai_doaj_org_article_445b3227d3d94d6d92761b2fe2e87dad
source Springer Nature - SpringerLink Journals - Fully Open Access ; Publicly Available Content (ProQuest)
subjects Analysis
Applications of Mathematics
Cauchy inequality
Convergence of series
Mathematics
Mathematics and Statistics
Möbius addition
Möbius scalar multiplication
Real numbers
title A Cauchy type inequality for Möbius operations
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-05T06%3A25%3A03IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_doaj_&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=A%20Cauchy%20type%20inequality%20for%20M%C3%B6bius%20operations&rft.jtitle=Journal%20of%20inequalities%20and%20applications&rft.au=Watanabe,%20Keiichi&rft.date=2018&rft.volume=2018&rft.issue=1&rft.spage=1&rft.epage=9&rft.pages=1-9&rft.artnum=97&rft.issn=1029-242X&rft.eissn=1029-242X&rft_id=info:doi/10.1186/s13660-018-1690-2&rft_dat=%3Cproquest_doaj_%3E2030106497%3C/proquest_doaj_%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c536t-3330c376b7048251a87a5d1edef840c68ea9d220d0f2ed3bc29eebec73a388433%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=2030106497&rft_id=info:pmid/29720845&rfr_iscdi=true