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Stability of an AQCQ functional equation in non-Archimedean (n,β)-normed spaces
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| Zeitschriftentitel: | Demonstratio Mathematica |
|---|---|
| Personen und Körperschaften: | , , |
| In: | Demonstratio Mathematica, 52, 2019, 1, S. 130-146 |
| Format: | E-Article |
| Sprache: | Englisch |
| veröffentlicht: |
Walter de Gruyter GmbH
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| Schlagwörter: |
| author_facet |
Liu, Yachai Yang, Xiuzhong Liu, Guofen Liu, Yachai Yang, Xiuzhong Liu, Guofen |
|---|---|
| author |
Liu, Yachai Yang, Xiuzhong Liu, Guofen |
| spellingShingle |
Liu, Yachai Yang, Xiuzhong Liu, Guofen Demonstratio Mathematica Stability of an AQCQ functional equation in non-Archimedean (n,β)-normed spaces General Mathematics |
| author_sort |
liu, yachai |
| spelling |
Liu, Yachai Yang, Xiuzhong Liu, Guofen 2391-4661 Walter de Gruyter GmbH General Mathematics http://dx.doi.org/10.1515/dema-2019-0009 <jats:title>Abstract</jats:title><jats:p>In this paper, we adopt direct method to prove the Hyers-Ulam-Rassias stability of an additivequadratic-cubic-quartic functional equation</jats:p><jats:p><jats:disp-formula><jats:alternatives><jats:graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_dema-2019-0009_eq_001.png" /><m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="block"><m:mrow><m:mi>f</m:mi><m:mo stretchy="false">(</m:mo><m:mi>x</m:mi><m:mo>+</m:mo><m:mn>2</m:mn><m:mi>y</m:mi><m:mo stretchy="false">)</m:mo><m:mo>+</m:mo><m:mi>f</m:mi><m:mo stretchy="false">(</m:mo><m:mi>x</m:mi><m:mo>−</m:mo><m:mn>2</m:mn><m:mi>y</m:mi><m:mo stretchy="false">)</m:mo><m:mo>=</m:mo><m:mn>4</m:mn><m:mi>f</m:mi><m:mo stretchy="false">(</m:mo><m:mi>x</m:mi><m:mo>+</m:mo><m:mi>y</m:mi><m:mo stretchy="false">)</m:mo><m:mo>+</m:mo><m:mn>4</m:mn><m:mi>f</m:mi><m:mo stretchy="false">(</m:mo><m:mi>x</m:mi><m:mo>−</m:mo><m:mi>y</m:mi><m:mo stretchy="false">)</m:mo><m:mo>−</m:mo><m:mn>6</m:mn><m:mi>f</m:mi><m:mo stretchy="false">(</m:mo><m:mi>x</m:mi><m:mo stretchy="false">)</m:mo><m:mo>+</m:mo><m:mi>f</m:mi><m:mo stretchy="false">(</m:mo><m:mn>2</m:mn><m:mi>y</m:mi><m:mo stretchy="false">)</m:mo><m:mo>+</m:mo><m:mi>f</m:mi><m:mo stretchy="false">(</m:mo><m:mo>−</m:mo><m:mn>2</m:mn><m:mi>y</m:mi><m:mo stretchy="false">)</m:mo><m:mo>−</m:mo><m:mn>4</m:mn><m:mi>f</m:mi><m:mo stretchy="false">(</m:mo><m:mi>y</m:mi><m:mo stretchy="false">)</m:mo><m:mo>−</m:mo><m:mn>4</m:mn><m:mi>f</m:mi><m:mo stretchy="false">(</m:mo><m:mo>−</m:mo><m:mi>y</m:mi><m:mo stretchy="false">)</m:mo></m:mrow></m:math><jats:tex-math>$$f(x + 2y) + f(x - 2y) = 4f(x + y) + 4f(x - y) - 6f(x) + f(2y) + f( - 2y) - 4f(y) - 4f( - y)$$</jats:tex-math></jats:alternatives></jats:disp-formula></jats:p><jats:p>in non-Archimedean (<jats:italic>n</jats:italic>,<jats:italic>β</jats:italic>)-normed spaces.</jats:p> Stability of an AQCQ functional equation in non-Archimedean (<i>n</i>,<i>β</i>)-normed spaces Demonstratio Mathematica |
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10.1515/dema-2019-0009 |
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ElectronicArticle |
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ai-49-aHR0cDovL2R4LmRvaS5vcmcvMTAuMTUxNS9kZW1hLTIwMTktMDAwOQ |
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DE-L229 DE-D275 DE-Bn3 DE-Brt1 DE-Zwi2 DE-D161 DE-Gla1 DE-Zi4 DE-15 DE-Pl11 DE-Rs1 DE-105 DE-14 DE-Ch1 |
| imprint |
Walter de Gruyter GmbH, 2019 |
| imprint_str_mv |
Walter de Gruyter GmbH, 2019 |
| issn |
2391-4661 |
| issn_str_mv |
2391-4661 |
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English |
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Walter de Gruyter GmbH (CrossRef) |
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liu2019stabilityofanaqcqfunctionalequationinnonarchimedeannbnormedspaces |
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2019 |
| publisher |
Walter de Gruyter GmbH |
| recordtype |
ai |
| record_format |
ai |
| series |
Demonstratio Mathematica |
| source_id |
49 |
| title |
Stability of an AQCQ functional equation in non-Archimedean (n,β)-normed spaces |
| title_unstemmed |
Stability of an AQCQ functional equation in non-Archimedean (n,β)-normed spaces |
| title_full |
Stability of an AQCQ functional equation in non-Archimedean (n,β)-normed spaces |
| title_fullStr |
Stability of an AQCQ functional equation in non-Archimedean (n,β)-normed spaces |
| title_full_unstemmed |
Stability of an AQCQ functional equation in non-Archimedean (n,β)-normed spaces |
| title_short |
Stability of an AQCQ functional equation in non-Archimedean (n,β)-normed spaces |
| title_sort |
stability of an aqcq functional equation in non-archimedean (<i>n</i>,<i>β</i>)-normed spaces |
| topic |
General Mathematics |
| url |
http://dx.doi.org/10.1515/dema-2019-0009 |
| publishDate |
2019 |
| physical |
130-146 |
| description |
<jats:title>Abstract</jats:title><jats:p>In this paper, we adopt direct method to prove the Hyers-Ulam-Rassias stability of an additivequadratic-cubic-quartic functional equation</jats:p><jats:p><jats:disp-formula><jats:alternatives><jats:graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_dema-2019-0009_eq_001.png" /><m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="block"><m:mrow><m:mi>f</m:mi><m:mo stretchy="false">(</m:mo><m:mi>x</m:mi><m:mo>+</m:mo><m:mn>2</m:mn><m:mi>y</m:mi><m:mo stretchy="false">)</m:mo><m:mo>+</m:mo><m:mi>f</m:mi><m:mo stretchy="false">(</m:mo><m:mi>x</m:mi><m:mo>−</m:mo><m:mn>2</m:mn><m:mi>y</m:mi><m:mo stretchy="false">)</m:mo><m:mo>=</m:mo><m:mn>4</m:mn><m:mi>f</m:mi><m:mo stretchy="false">(</m:mo><m:mi>x</m:mi><m:mo>+</m:mo><m:mi>y</m:mi><m:mo stretchy="false">)</m:mo><m:mo>+</m:mo><m:mn>4</m:mn><m:mi>f</m:mi><m:mo stretchy="false">(</m:mo><m:mi>x</m:mi><m:mo>−</m:mo><m:mi>y</m:mi><m:mo stretchy="false">)</m:mo><m:mo>−</m:mo><m:mn>6</m:mn><m:mi>f</m:mi><m:mo stretchy="false">(</m:mo><m:mi>x</m:mi><m:mo stretchy="false">)</m:mo><m:mo>+</m:mo><m:mi>f</m:mi><m:mo stretchy="false">(</m:mo><m:mn>2</m:mn><m:mi>y</m:mi><m:mo stretchy="false">)</m:mo><m:mo>+</m:mo><m:mi>f</m:mi><m:mo stretchy="false">(</m:mo><m:mo>−</m:mo><m:mn>2</m:mn><m:mi>y</m:mi><m:mo stretchy="false">)</m:mo><m:mo>−</m:mo><m:mn>4</m:mn><m:mi>f</m:mi><m:mo stretchy="false">(</m:mo><m:mi>y</m:mi><m:mo stretchy="false">)</m:mo><m:mo>−</m:mo><m:mn>4</m:mn><m:mi>f</m:mi><m:mo stretchy="false">(</m:mo><m:mo>−</m:mo><m:mi>y</m:mi><m:mo stretchy="false">)</m:mo></m:mrow></m:math><jats:tex-math>$$f(x + 2y) + f(x - 2y) = 4f(x + y) + 4f(x - y) - 6f(x) + f(2y) + f( - 2y) - 4f(y) - 4f( - y)$$</jats:tex-math></jats:alternatives></jats:disp-formula></jats:p><jats:p>in non-Archimedean (<jats:italic>n</jats:italic>,<jats:italic>β</jats:italic>)-normed spaces.</jats:p> |
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| description | <jats:title>Abstract</jats:title><jats:p>In this paper, we adopt direct method to prove the Hyers-Ulam-Rassias stability of an additivequadratic-cubic-quartic functional equation</jats:p><jats:p><jats:disp-formula><jats:alternatives><jats:graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_dema-2019-0009_eq_001.png" /><m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="block"><m:mrow><m:mi>f</m:mi><m:mo stretchy="false">(</m:mo><m:mi>x</m:mi><m:mo>+</m:mo><m:mn>2</m:mn><m:mi>y</m:mi><m:mo stretchy="false">)</m:mo><m:mo>+</m:mo><m:mi>f</m:mi><m:mo stretchy="false">(</m:mo><m:mi>x</m:mi><m:mo>−</m:mo><m:mn>2</m:mn><m:mi>y</m:mi><m:mo stretchy="false">)</m:mo><m:mo>=</m:mo><m:mn>4</m:mn><m:mi>f</m:mi><m:mo stretchy="false">(</m:mo><m:mi>x</m:mi><m:mo>+</m:mo><m:mi>y</m:mi><m:mo stretchy="false">)</m:mo><m:mo>+</m:mo><m:mn>4</m:mn><m:mi>f</m:mi><m:mo stretchy="false">(</m:mo><m:mi>x</m:mi><m:mo>−</m:mo><m:mi>y</m:mi><m:mo stretchy="false">)</m:mo><m:mo>−</m:mo><m:mn>6</m:mn><m:mi>f</m:mi><m:mo stretchy="false">(</m:mo><m:mi>x</m:mi><m:mo stretchy="false">)</m:mo><m:mo>+</m:mo><m:mi>f</m:mi><m:mo stretchy="false">(</m:mo><m:mn>2</m:mn><m:mi>y</m:mi><m:mo stretchy="false">)</m:mo><m:mo>+</m:mo><m:mi>f</m:mi><m:mo stretchy="false">(</m:mo><m:mo>−</m:mo><m:mn>2</m:mn><m:mi>y</m:mi><m:mo stretchy="false">)</m:mo><m:mo>−</m:mo><m:mn>4</m:mn><m:mi>f</m:mi><m:mo stretchy="false">(</m:mo><m:mi>y</m:mi><m:mo stretchy="false">)</m:mo><m:mo>−</m:mo><m:mn>4</m:mn><m:mi>f</m:mi><m:mo stretchy="false">(</m:mo><m:mo>−</m:mo><m:mi>y</m:mi><m:mo stretchy="false">)</m:mo></m:mrow></m:math><jats:tex-math>$$f(x + 2y) + f(x - 2y) = 4f(x + y) + 4f(x - y) - 6f(x) + f(2y) + f( - 2y) - 4f(y) - 4f( - y)$$</jats:tex-math></jats:alternatives></jats:disp-formula></jats:p><jats:p>in non-Archimedean (<jats:italic>n</jats:italic>,<jats:italic>β</jats:italic>)-normed spaces.</jats:p> |
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| imprint | Walter de Gruyter GmbH, 2019 |
| imprint_str_mv | Walter de Gruyter GmbH, 2019 |
| institution | DE-L229, DE-D275, DE-Bn3, DE-Brt1, DE-Zwi2, DE-D161, DE-Gla1, DE-Zi4, DE-15, DE-Pl11, DE-Rs1, DE-105, DE-14, DE-Ch1 |
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| spelling | Liu, Yachai Yang, Xiuzhong Liu, Guofen 2391-4661 Walter de Gruyter GmbH General Mathematics http://dx.doi.org/10.1515/dema-2019-0009 <jats:title>Abstract</jats:title><jats:p>In this paper, we adopt direct method to prove the Hyers-Ulam-Rassias stability of an additivequadratic-cubic-quartic functional equation</jats:p><jats:p><jats:disp-formula><jats:alternatives><jats:graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_dema-2019-0009_eq_001.png" /><m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="block"><m:mrow><m:mi>f</m:mi><m:mo stretchy="false">(</m:mo><m:mi>x</m:mi><m:mo>+</m:mo><m:mn>2</m:mn><m:mi>y</m:mi><m:mo stretchy="false">)</m:mo><m:mo>+</m:mo><m:mi>f</m:mi><m:mo stretchy="false">(</m:mo><m:mi>x</m:mi><m:mo>−</m:mo><m:mn>2</m:mn><m:mi>y</m:mi><m:mo stretchy="false">)</m:mo><m:mo>=</m:mo><m:mn>4</m:mn><m:mi>f</m:mi><m:mo stretchy="false">(</m:mo><m:mi>x</m:mi><m:mo>+</m:mo><m:mi>y</m:mi><m:mo stretchy="false">)</m:mo><m:mo>+</m:mo><m:mn>4</m:mn><m:mi>f</m:mi><m:mo stretchy="false">(</m:mo><m:mi>x</m:mi><m:mo>−</m:mo><m:mi>y</m:mi><m:mo stretchy="false">)</m:mo><m:mo>−</m:mo><m:mn>6</m:mn><m:mi>f</m:mi><m:mo stretchy="false">(</m:mo><m:mi>x</m:mi><m:mo stretchy="false">)</m:mo><m:mo>+</m:mo><m:mi>f</m:mi><m:mo stretchy="false">(</m:mo><m:mn>2</m:mn><m:mi>y</m:mi><m:mo stretchy="false">)</m:mo><m:mo>+</m:mo><m:mi>f</m:mi><m:mo stretchy="false">(</m:mo><m:mo>−</m:mo><m:mn>2</m:mn><m:mi>y</m:mi><m:mo stretchy="false">)</m:mo><m:mo>−</m:mo><m:mn>4</m:mn><m:mi>f</m:mi><m:mo stretchy="false">(</m:mo><m:mi>y</m:mi><m:mo stretchy="false">)</m:mo><m:mo>−</m:mo><m:mn>4</m:mn><m:mi>f</m:mi><m:mo stretchy="false">(</m:mo><m:mo>−</m:mo><m:mi>y</m:mi><m:mo stretchy="false">)</m:mo></m:mrow></m:math><jats:tex-math>$$f(x + 2y) + f(x - 2y) = 4f(x + y) + 4f(x - y) - 6f(x) + f(2y) + f( - 2y) - 4f(y) - 4f( - y)$$</jats:tex-math></jats:alternatives></jats:disp-formula></jats:p><jats:p>in non-Archimedean (<jats:italic>n</jats:italic>,<jats:italic>β</jats:italic>)-normed spaces.</jats:p> Stability of an AQCQ functional equation in non-Archimedean (<i>n</i>,<i>β</i>)-normed spaces Demonstratio Mathematica |
| spellingShingle | Liu, Yachai, Yang, Xiuzhong, Liu, Guofen, Demonstratio Mathematica, Stability of an AQCQ functional equation in non-Archimedean (n,β)-normed spaces, General Mathematics |
| title | Stability of an AQCQ functional equation in non-Archimedean (n,β)-normed spaces |
| title_full | Stability of an AQCQ functional equation in non-Archimedean (n,β)-normed spaces |
| title_fullStr | Stability of an AQCQ functional equation in non-Archimedean (n,β)-normed spaces |
| title_full_unstemmed | Stability of an AQCQ functional equation in non-Archimedean (n,β)-normed spaces |
| title_short | Stability of an AQCQ functional equation in non-Archimedean (n,β)-normed spaces |
| title_sort | stability of an aqcq functional equation in non-archimedean (<i>n</i>,<i>β</i>)-normed spaces |
| title_unstemmed | Stability of an AQCQ functional equation in non-Archimedean (n,β)-normed spaces |
| topic | General Mathematics |
| url | http://dx.doi.org/10.1515/dema-2019-0009 |