On the stability of an AQCQ-functional equation in random normed spaces
<p>Abstract</p> <p>In this paper, we prove the Hyers-Ulam stability of the following additive-quadratic-cubic-quartic functional equation</p> <p> <display-formula> <m:math name="1029-242X-2011-34-i1" xmlns:m="http://www.w3.org/1998/Math/MathML&qu...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2011-01-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://www.journalofinequalitiesandapplications.com/content/2011/1/34 |
| _version_ | 1811250351341305856 |
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| author | Jang Sun Young Shin Dong Yun Lee Jung Rye Park Choonkil |
| author_facet | Jang Sun Young Shin Dong Yun Lee Jung Rye Park Choonkil |
| author_sort | Jang Sun Young |
| collection | DOAJ |
| description | <p>Abstract</p> <p>In this paper, we prove the Hyers-Ulam stability of the following additive-quadratic-cubic-quartic functional equation</p> <p> <display-formula> <m:math name="1029-242X-2011-34-i1" xmlns:m="http://www.w3.org/1998/Math/MathML"><m:mtable columnalign="left" class="align"> <m:mtr> <m:mtd columnalign="right" class="align-odd"> <m:mi>f</m:mi> <m:mrow> <m:mo class="MathClass-open">(</m:mo> <m:mrow> <m:mi>x</m:mi> <m:mo class="MathClass-bin">+</m:mo> <m:mn>2</m:mn> <m:mi>y</m:mi> </m:mrow> <m:mo class="MathClass-close">)</m:mo> </m:mrow> <m:mo class="MathClass-bin">+</m:mo> <m:mi>f</m:mi> <m:mrow> <m:mo class="MathClass-open">(</m:mo> <m:mrow> <m:mi>x</m:mi> <m:mo class="MathClass-bin">-</m:mo> <m:mn>2</m:mn> <m:mi>y</m:mi> </m:mrow> <m:mo class="MathClass-close">)</m:mo> </m:mrow> </m:mtd> <m:mtd class="align-even"> <m:mo class="MathClass-rel">=</m:mo> <m:mn>4</m:mn> <m:mi>f</m:mi> <m:mrow> <m:mo class="MathClass-open">(</m:mo> <m:mrow> <m:mi>x</m:mi> <m:mo class="MathClass-bin">+</m:mo> <m:mi>y</m:mi> </m:mrow> <m:mo class="MathClass-close">)</m:mo> </m:mrow> <m:mo class="MathClass-bin">+</m:mo> <m:mn>4</m:mn> <m:mi>f</m:mi> <m:mrow> <m:mo class="MathClass-open">(</m:mo> <m:mrow> <m:mi>x</m:mi> <m:mo class="MathClass-bin">-</m:mo> <m:mi>y</m:mi> </m:mrow> <m:mo class="MathClass-close">)</m:mo> </m:mrow> <m:mo class="MathClass-bin">-</m:mo> <m:mn>6</m:mn> <m:mi>f</m:mi> <m:mrow> <m:mo class="MathClass-open">(</m:mo> <m:mrow> <m:mi>x</m:mi> </m:mrow> <m:mo class="MathClass-close">)</m:mo> </m:mrow> <m:mspace width="2em"/> </m:mtd> <m:mtd columnalign="right" class="align-label"> <m:mstyle id="x1-2r1" class="label"/> <m:mstyle class="maketag"> <m:mtext>(1)</m:mtext> </m:mstyle> </m:mtd> </m:mtr> <m:mtr> <m:mtd columnalign="right" class="align-odd"/> <m:mtd class="align-even"> <m:mo class="MathClass-bin">+</m:mo> <m:mi>f</m:mi> <m:mrow> <m:mo class="MathClass-open">(</m:mo> <m:mrow> <m:mn>2</m:mn> <m:mi>y</m:mi> </m:mrow> <m:mo class="MathClass-close">)</m:mo> </m:mrow> <m:mo class="MathClass-bin">+</m:mo> <m:mi>f</m:mi> <m:mrow> <m:mo class="MathClass-open">(</m:mo> <m:mrow> <m:mo class="MathClass-bin">-</m:mo> <m:mn>2</m:mn> <m:mi>y</m:mi> </m:mrow> <m:mo class="MathClass-close">)</m:mo> </m:mrow> <m:mo class="MathClass-bin">-</m:mo> <m:mn>4</m:mn> <m:mi>f</m:mi> <m:mrow> <m:mo class="MathClass-open">(</m:mo> <m:mrow> <m:mi>y</m:mi> </m:mrow> <m:mo class="MathClass-close">)</m:mo> </m:mrow> <m:mo class="MathClass-bin">-</m:mo> <m:mn>4</m:mn> <m:mi>f</m:mi> <m:mrow> <m:mo class="MathClass-open">(</m:mo> <m:mrow> <m:mo class="MathClass-bin">-</m:mo> <m:mi>y</m:mi> </m:mrow> <m:mo class="MathClass-close">)</m:mo> </m:mrow> <m:mspace width="2em"/> </m:mtd> <m:mtd columnalign="right" class="align-label"> <m:mstyle id="x1-3r2" class="label"/> <m:mstyle class="maketag"> <m:mtext>(2)</m:mtext> </m:mstyle> </m:mtd> </m:mtr> <m:mtr> <m:mtd columnalign="right" class="align-odd"/> <m:mtd class="align-even"> <m:mspace width="2em"/> </m:mtd> <m:mtd columnalign="right" class="align-label"> <m:mstyle id="x1-4r3" class="label"/> <m:mstyle class="maketag"> <m:mtext>(3)</m:mtext> </m:mstyle> </m:mtd> </m:mtr> </m:mtable> </m:math> </display-formula> </p> <p>in random normed spaces.</p> <p> <b>2010 Mathematics Subject Classification: 46S40; 39B52; 54E70</b> </p> |
| first_indexed | 2024-04-12T16:03:32Z |
| format | Article |
| id | doaj.art-929f906e2282456d988b00062eac5d95 |
| institution | Directory Open Access Journal |
| issn | 1025-5834 1029-242X |
| language | English |
| last_indexed | 2024-04-12T16:03:32Z |
| publishDate | 2011-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-929f906e2282456d988b00062eac5d952022-12-22T03:26:08ZengSpringerOpenJournal of Inequalities and Applications1025-58341029-242X2011-01-012011134On the stability of an AQCQ-functional equation in random normed spacesJang Sun YoungShin Dong YunLee Jung RyePark Choonkil<p>Abstract</p> <p>In this paper, we prove the Hyers-Ulam stability of the following additive-quadratic-cubic-quartic functional equation</p> <p> <display-formula> <m:math name="1029-242X-2011-34-i1" xmlns:m="http://www.w3.org/1998/Math/MathML"><m:mtable columnalign="left" class="align"> <m:mtr> <m:mtd columnalign="right" class="align-odd"> <m:mi>f</m:mi> <m:mrow> <m:mo class="MathClass-open">(</m:mo> <m:mrow> <m:mi>x</m:mi> <m:mo class="MathClass-bin">+</m:mo> <m:mn>2</m:mn> <m:mi>y</m:mi> </m:mrow> <m:mo class="MathClass-close">)</m:mo> </m:mrow> <m:mo class="MathClass-bin">+</m:mo> <m:mi>f</m:mi> <m:mrow> <m:mo class="MathClass-open">(</m:mo> <m:mrow> <m:mi>x</m:mi> <m:mo class="MathClass-bin">-</m:mo> <m:mn>2</m:mn> <m:mi>y</m:mi> </m:mrow> <m:mo class="MathClass-close">)</m:mo> </m:mrow> </m:mtd> <m:mtd class="align-even"> <m:mo class="MathClass-rel">=</m:mo> <m:mn>4</m:mn> <m:mi>f</m:mi> <m:mrow> <m:mo class="MathClass-open">(</m:mo> <m:mrow> <m:mi>x</m:mi> <m:mo class="MathClass-bin">+</m:mo> <m:mi>y</m:mi> </m:mrow> <m:mo class="MathClass-close">)</m:mo> </m:mrow> <m:mo class="MathClass-bin">+</m:mo> <m:mn>4</m:mn> <m:mi>f</m:mi> <m:mrow> <m:mo class="MathClass-open">(</m:mo> <m:mrow> <m:mi>x</m:mi> <m:mo class="MathClass-bin">-</m:mo> <m:mi>y</m:mi> </m:mrow> <m:mo class="MathClass-close">)</m:mo> </m:mrow> <m:mo class="MathClass-bin">-</m:mo> <m:mn>6</m:mn> <m:mi>f</m:mi> <m:mrow> <m:mo class="MathClass-open">(</m:mo> <m:mrow> <m:mi>x</m:mi> </m:mrow> <m:mo class="MathClass-close">)</m:mo> </m:mrow> <m:mspace width="2em"/> </m:mtd> <m:mtd columnalign="right" class="align-label"> <m:mstyle id="x1-2r1" class="label"/> <m:mstyle class="maketag"> <m:mtext>(1)</m:mtext> </m:mstyle> </m:mtd> </m:mtr> <m:mtr> <m:mtd columnalign="right" class="align-odd"/> <m:mtd class="align-even"> <m:mo class="MathClass-bin">+</m:mo> <m:mi>f</m:mi> <m:mrow> <m:mo class="MathClass-open">(</m:mo> <m:mrow> <m:mn>2</m:mn> <m:mi>y</m:mi> </m:mrow> <m:mo class="MathClass-close">)</m:mo> </m:mrow> <m:mo class="MathClass-bin">+</m:mo> <m:mi>f</m:mi> <m:mrow> <m:mo class="MathClass-open">(</m:mo> <m:mrow> <m:mo class="MathClass-bin">-</m:mo> <m:mn>2</m:mn> <m:mi>y</m:mi> </m:mrow> <m:mo class="MathClass-close">)</m:mo> </m:mrow> <m:mo class="MathClass-bin">-</m:mo> <m:mn>4</m:mn> <m:mi>f</m:mi> <m:mrow> <m:mo class="MathClass-open">(</m:mo> <m:mrow> <m:mi>y</m:mi> </m:mrow> <m:mo class="MathClass-close">)</m:mo> </m:mrow> <m:mo class="MathClass-bin">-</m:mo> <m:mn>4</m:mn> <m:mi>f</m:mi> <m:mrow> <m:mo class="MathClass-open">(</m:mo> <m:mrow> <m:mo class="MathClass-bin">-</m:mo> <m:mi>y</m:mi> </m:mrow> <m:mo class="MathClass-close">)</m:mo> </m:mrow> <m:mspace width="2em"/> </m:mtd> <m:mtd columnalign="right" class="align-label"> <m:mstyle id="x1-3r2" class="label"/> <m:mstyle class="maketag"> <m:mtext>(2)</m:mtext> </m:mstyle> </m:mtd> </m:mtr> <m:mtr> <m:mtd columnalign="right" class="align-odd"/> <m:mtd class="align-even"> <m:mspace width="2em"/> </m:mtd> <m:mtd columnalign="right" class="align-label"> <m:mstyle id="x1-4r3" class="label"/> <m:mstyle class="maketag"> <m:mtext>(3)</m:mtext> </m:mstyle> </m:mtd> </m:mtr> </m:mtable> </m:math> </display-formula> </p> <p>in random normed spaces.</p> <p> <b>2010 Mathematics Subject Classification: 46S40; 39B52; 54E70</b> </p>http://www.journalofinequalitiesandapplications.com/content/2011/1/34random normed spaceadditive-quadratic-cubic-quartic functional equationHyers-Ulam stability |
| spellingShingle | Jang Sun Young Shin Dong Yun Lee Jung Rye Park Choonkil On the stability of an AQCQ-functional equation in random normed spaces Journal of Inequalities and Applications random normed space additive-quadratic-cubic-quartic functional equation Hyers-Ulam stability |
| title | On the stability of an AQCQ-functional equation in random normed spaces |
| title_full | On the stability of an AQCQ-functional equation in random normed spaces |
| title_fullStr | On the stability of an AQCQ-functional equation in random normed spaces |
| title_full_unstemmed | On the stability of an AQCQ-functional equation in random normed spaces |
| title_short | On the stability of an AQCQ-functional equation in random normed spaces |
| title_sort | on the stability of an aqcq functional equation in random normed spaces |
| topic | random normed space additive-quadratic-cubic-quartic functional equation Hyers-Ulam stability |
| url | http://www.journalofinequalitiesandapplications.com/content/2011/1/34 |
| work_keys_str_mv | AT jangsunyoung onthestabilityofanaqcqfunctionalequationinrandomnormedspaces AT shindongyun onthestabilityofanaqcqfunctionalequationinrandomnormedspaces AT leejungrye onthestabilityofanaqcqfunctionalequationinrandomnormedspaces AT parkchoonkil onthestabilityofanaqcqfunctionalequationinrandomnormedspaces |