An Integral Mean Value Theorem concerning Two Continuous Functions and Its Stability
The aim of this paper is to investigate an integral mean value theorem proposed by one of the references of this paper. Unfortunately, the proof contains a gap. First, we present a counterexample which shows that this theorem fails in this form. Then, we present two improved versions of this theorem...
Gespeichert in:
| Veröffentlicht in: | International journal of analysis 2015-01, Vol.2015, p.1-4 |
|---|---|
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 4 |
|---|---|
| container_issue | |
| container_start_page | 1 |
| container_title | International journal of analysis |
| container_volume | 2015 |
| creator | Mihai, Monea |
| description | The aim of this paper is to investigate an integral mean value theorem proposed by one of the references of this paper. Unfortunately, the proof contains a gap. First, we present a counterexample which shows that this theorem fails in this form. Then, we present two improved versions of this theorem. The stability of the mean point arising from the second result concludes this paper. |
| doi_str_mv | 10.1155/2015/894625 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_1762093314</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>1762093314</sourcerecordid><originalsourceid>FETCH-LOGICAL-c296t-d8e2450c44faf7070d2297463e6aaabda4b55f9f87be1851b608057ab07c58ae3</originalsourceid><addsrcrecordid>eNp90EFLwzAUB_AgCo65k18g4EWUuiRN2uQ4htPBxINVvJU0TbeMLplJyti3t6PiwYOn9w4_Hv_3B-AaoweMGZsShNmUC5oRdgZGJMU0oULw89-df16CSQhbhBAmnKWUj0Axs3Bpo1572cIXLS38kG2nYbHRzusdVM4q7a2xa1gcHJw7G43tXBfgorMqGmcDlLaGyxjgW5SVaU08XoGLRrZBT37mGLwvHov5c7J6fVrOZ6tEEZHFpOaaUIYUpY1scpSjmhCR0yzVmZSyqiWtGGtEw_NKY85wlSGOWC4rlCvGpU7H4Ha4u_fuq9MhljsTlG5baXUfscR5RpBI--97evOHbl3nbZ-uVwSnmAme9up-UMq7ELxuyr03O-mPJUblqeTyVHI5lNzru0FvjK3lwfyLvwFf1Ho1</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1721315983</pqid></control><display><type>article</type><title>An Integral Mean Value Theorem concerning Two Continuous Functions and Its Stability</title><source>Wiley Online Library Open Access</source><source>Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals</source><source>Alma/SFX Local Collection</source><creator>Mihai, Monea</creator><contributor>Hu, Yaozhong</contributor><creatorcontrib>Mihai, Monea ; Hu, Yaozhong</creatorcontrib><description>The aim of this paper is to investigate an integral mean value theorem proposed by one of the references of this paper. Unfortunately, the proof contains a gap. First, we present a counterexample which shows that this theorem fails in this form. Then, we present two improved versions of this theorem. The stability of the mean point arising from the second result concludes this paper.</description><identifier>ISSN: 2314-498X</identifier><identifier>EISSN: 2314-4998</identifier><identifier>DOI: 10.1155/2015/894625</identifier><language>eng</language><publisher>Cairo: Hindawi Publishing Corporation</publisher><subject>Integrals ; Proving ; Stability ; Theorems</subject><ispartof>International journal of analysis, 2015-01, Vol.2015, p.1-4</ispartof><rights>Copyright © 2015 Monea Mihai.</rights><rights>Copyright © 2015 Monea Mihai. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c296t-d8e2450c44faf7070d2297463e6aaabda4b55f9f87be1851b608057ab07c58ae3</citedby><cites>FETCH-LOGICAL-c296t-d8e2450c44faf7070d2297463e6aaabda4b55f9f87be1851b608057ab07c58ae3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,776,780,27903,27904</link.rule.ids></links><search><contributor>Hu, Yaozhong</contributor><creatorcontrib>Mihai, Monea</creatorcontrib><title>An Integral Mean Value Theorem concerning Two Continuous Functions and Its Stability</title><title>International journal of analysis</title><description>The aim of this paper is to investigate an integral mean value theorem proposed by one of the references of this paper. Unfortunately, the proof contains a gap. First, we present a counterexample which shows that this theorem fails in this form. Then, we present two improved versions of this theorem. The stability of the mean point arising from the second result concludes this paper.</description><subject>Integrals</subject><subject>Proving</subject><subject>Stability</subject><subject>Theorems</subject><issn>2314-498X</issn><issn>2314-4998</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2015</creationdate><recordtype>article</recordtype><sourceid>RHX</sourceid><sourceid>BENPR</sourceid><recordid>eNp90EFLwzAUB_AgCo65k18g4EWUuiRN2uQ4htPBxINVvJU0TbeMLplJyti3t6PiwYOn9w4_Hv_3B-AaoweMGZsShNmUC5oRdgZGJMU0oULw89-df16CSQhbhBAmnKWUj0Axs3Bpo1572cIXLS38kG2nYbHRzusdVM4q7a2xa1gcHJw7G43tXBfgorMqGmcDlLaGyxjgW5SVaU08XoGLRrZBT37mGLwvHov5c7J6fVrOZ6tEEZHFpOaaUIYUpY1scpSjmhCR0yzVmZSyqiWtGGtEw_NKY85wlSGOWC4rlCvGpU7H4Ha4u_fuq9MhljsTlG5baXUfscR5RpBI--97evOHbl3nbZ-uVwSnmAme9up-UMq7ELxuyr03O-mPJUblqeTyVHI5lNzru0FvjK3lwfyLvwFf1Ho1</recordid><startdate>20150101</startdate><enddate>20150101</enddate><creator>Mihai, Monea</creator><general>Hindawi Publishing Corporation</general><general>Hindawi Limited</general><scope>RHU</scope><scope>RHW</scope><scope>RHX</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7SC</scope><scope>7TB</scope><scope>7XB</scope><scope>8AL</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</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>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>M0N</scope><scope>M7S</scope><scope>P62</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>Q9U</scope></search><sort><creationdate>20150101</creationdate><title>An Integral Mean Value Theorem concerning Two Continuous Functions and Its Stability</title><author>Mihai, Monea</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c296t-d8e2450c44faf7070d2297463e6aaabda4b55f9f87be1851b608057ab07c58ae3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2015</creationdate><topic>Integrals</topic><topic>Proving</topic><topic>Stability</topic><topic>Theorems</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Mihai, Monea</creatorcontrib><collection>Hindawi Publishing Complete</collection><collection>Hindawi Publishing Subscription Journals</collection><collection>Hindawi Publishing Open Access</collection><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>Computing Database (Alumni Edition)</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</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>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>Computing Database</collection><collection>Engineering Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>Publicly Available Content Database</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>ProQuest Central Basic</collection><jtitle>International journal of analysis</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Mihai, Monea</au><au>Hu, Yaozhong</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>An Integral Mean Value Theorem concerning Two Continuous Functions and Its Stability</atitle><jtitle>International journal of analysis</jtitle><date>2015-01-01</date><risdate>2015</risdate><volume>2015</volume><spage>1</spage><epage>4</epage><pages>1-4</pages><issn>2314-498X</issn><eissn>2314-4998</eissn><abstract>The aim of this paper is to investigate an integral mean value theorem proposed by one of the references of this paper. Unfortunately, the proof contains a gap. First, we present a counterexample which shows that this theorem fails in this form. Then, we present two improved versions of this theorem. The stability of the mean point arising from the second result concludes this paper.</abstract><cop>Cairo</cop><pub>Hindawi Publishing Corporation</pub><doi>10.1155/2015/894625</doi><tpages>4</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 2314-498X |
| ispartof | International journal of analysis, 2015-01, Vol.2015, p.1-4 |
| issn | 2314-498X 2314-4998 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_1762093314 |
| source | Wiley Online Library Open Access; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; Alma/SFX Local Collection |
| subjects | Integrals Proving Stability Theorems |
| title | An Integral Mean Value Theorem concerning Two Continuous Functions and Its Stability |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-28T05%3A50%3A30IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=An%20Integral%20Mean%20Value%20Theorem%20concerning%20Two%20Continuous%20Functions%20and%20Its%20Stability&rft.jtitle=International%20journal%20of%20analysis&rft.au=Mihai,%20Monea&rft.date=2015-01-01&rft.volume=2015&rft.spage=1&rft.epage=4&rft.pages=1-4&rft.issn=2314-498X&rft.eissn=2314-4998&rft_id=info:doi/10.1155/2015/894625&rft_dat=%3Cproquest_cross%3E1762093314%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=1721315983&rft_id=info:pmid/&rfr_iscdi=true |