On the Ulam-Hyers stability of a quadratic functional equation
<p>Abstract</p> <p>The Ulam-Hyers stability problems of the following quadratic equation</p> <p> <display-formula> <m:math name="1029-242X-2011-79-i1" xmlns:m="http://www.w3.org/1998/Math/MathML"><m:msup> <m:mrow> <m:mi>...
| 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/2011/1/79 |
| _version_ | 1818528412741926912 |
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| author | Park Won-Gil Bae Jae-Hyeong Lee Sang-Baek |
| author_facet | Park Won-Gil Bae Jae-Hyeong Lee Sang-Baek |
| author_sort | Park Won-Gil |
| collection | DOAJ |
| description | <p>Abstract</p> <p>The Ulam-Hyers stability problems of the following quadratic equation</p> <p> <display-formula> <m:math name="1029-242X-2011-79-i1" xmlns:m="http://www.w3.org/1998/Math/MathML"><m:msup> <m:mrow> <m:mi>r</m:mi> </m:mrow> <m:mrow> <m:mn>2</m:mn> </m:mrow> </m:msup> <m:mi>f</m:mi> <m:mfenced separators="" open="(" close=")"> <m:mrow> <m:mfrac> <m:mrow> <m:mi>x</m:mi> <m:mo class="MathClass-bin">+</m:mo> <m:mi>y</m:mi> </m:mrow> <m:mrow> <m:mi>r</m:mi> </m:mrow> </m:mfrac> </m:mrow> </m:mfenced> <m:mo class="MathClass-bin">+</m:mo> <m:msup> <m:mrow> <m:mi>r</m:mi> </m:mrow> <m:mrow> <m:mn>2</m:mn> </m:mrow> </m:msup> <m:mi>f</m:mi> <m:mfenced separators="" open="(" close=")"> <m:mrow> <m:mfrac> <m:mrow> <m:mi>x</m:mi> <m:mo class="MathClass-bin">-</m:mo> <m:mi>y</m:mi> </m:mrow> <m:mrow> <m:mi>r</m:mi> </m:mrow> </m:mfrac> </m:mrow> </m:mfenced> <m:mo class="MathClass-rel">=</m:mo> <m:mn>2</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:mo class="MathClass-bin">+</m:mo> <m:mn>2</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-punc">,</m:mo> </m:math> </display-formula> </p> <p>where <it>r </it>is a nonzero rational number, shall be treated. The case <it>r </it>= 2 was introduced by J. M. Rassias in 1999. Furthermore, we prove the stability of the quadratic equation by using the fixed point method.</p> <p> <b>2010 Mathematics Subject Classification</b>: 39B22; 39B52; 39B72.</p> |
| first_indexed | 2024-12-11T06:49:27Z |
| format | Article |
| id | doaj.art-fefaed2198554d4781267c28fc7c37e8 |
| institution | Directory Open Access Journal |
| issn | 1025-5834 1029-242X |
| language | English |
| last_indexed | 2024-12-11T06:49:27Z |
| publishDate | 2011-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-fefaed2198554d4781267c28fc7c37e82022-12-22T01:16:57ZengSpringerOpenJournal of Inequalities and Applications1025-58341029-242X2011-01-012011179On the Ulam-Hyers stability of a quadratic functional equationPark Won-GilBae Jae-HyeongLee Sang-Baek<p>Abstract</p> <p>The Ulam-Hyers stability problems of the following quadratic equation</p> <p> <display-formula> <m:math name="1029-242X-2011-79-i1" xmlns:m="http://www.w3.org/1998/Math/MathML"><m:msup> <m:mrow> <m:mi>r</m:mi> </m:mrow> <m:mrow> <m:mn>2</m:mn> </m:mrow> </m:msup> <m:mi>f</m:mi> <m:mfenced separators="" open="(" close=")"> <m:mrow> <m:mfrac> <m:mrow> <m:mi>x</m:mi> <m:mo class="MathClass-bin">+</m:mo> <m:mi>y</m:mi> </m:mrow> <m:mrow> <m:mi>r</m:mi> </m:mrow> </m:mfrac> </m:mrow> </m:mfenced> <m:mo class="MathClass-bin">+</m:mo> <m:msup> <m:mrow> <m:mi>r</m:mi> </m:mrow> <m:mrow> <m:mn>2</m:mn> </m:mrow> </m:msup> <m:mi>f</m:mi> <m:mfenced separators="" open="(" close=")"> <m:mrow> <m:mfrac> <m:mrow> <m:mi>x</m:mi> <m:mo class="MathClass-bin">-</m:mo> <m:mi>y</m:mi> </m:mrow> <m:mrow> <m:mi>r</m:mi> </m:mrow> </m:mfrac> </m:mrow> </m:mfenced> <m:mo class="MathClass-rel">=</m:mo> <m:mn>2</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:mo class="MathClass-bin">+</m:mo> <m:mn>2</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-punc">,</m:mo> </m:math> </display-formula> </p> <p>where <it>r </it>is a nonzero rational number, shall be treated. The case <it>r </it>= 2 was introduced by J. M. Rassias in 1999. Furthermore, we prove the stability of the quadratic equation by using the fixed point method.</p> <p> <b>2010 Mathematics Subject Classification</b>: 39B22; 39B52; 39B72.</p>http://www.journalofinequalitiesandapplications.com/content/2011/1/79Hyers-Ulam stabilityquadratic function |
| spellingShingle | Park Won-Gil Bae Jae-Hyeong Lee Sang-Baek On the Ulam-Hyers stability of a quadratic functional equation Journal of Inequalities and Applications Hyers-Ulam stability quadratic function |
| title | On the Ulam-Hyers stability of a quadratic functional equation |
| title_full | On the Ulam-Hyers stability of a quadratic functional equation |
| title_fullStr | On the Ulam-Hyers stability of a quadratic functional equation |
| title_full_unstemmed | On the Ulam-Hyers stability of a quadratic functional equation |
| title_short | On the Ulam-Hyers stability of a quadratic functional equation |
| title_sort | on the ulam hyers stability of a quadratic functional equation |
| topic | Hyers-Ulam stability quadratic function |
| url | http://www.journalofinequalitiesandapplications.com/content/2011/1/79 |
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