On a Jensen-cubic functional equation and its Hyers–Ulam stability

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• 作者：Pei Sheng Ji ; Shu Juan Zhou ; Hai Yan Xue
• 关键词：Hyers–Ulam stability ; mixed cubic ; quadric function ; Jensen ; cubic functional equation ; 39B72 ; 47H14
• 刊名：Acta Mathematica Sinica
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：31
• 期：12
• 页码：1929-1940
• 全文大小：196 KB
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  [7]Eshaghi Gordji, M., Zolfaghari, S., Rassias, J. M., et al.: Solution and stability of a mixed type cubic and quartic functional equation in quasi-Banach spaces. Abstr. Appl. Anal., art. ID 417473, 14 pages (2009)
  [8]Jun, K. W., Kim, H. M.: The generalized Hyers–Ulam–Rassias stability of cubic functional equation. J. Math. Anal. Appl., 274(2002), 867-78 (2002)CrossRef MathSciNet MATH
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  [10]Park, W. G., Bae, J. H.: On a Cauchy–Jensen functional equation and its atability. J. Math. Anal. Appl., 323, 634-43 (2006)CrossRef MathSciNet MATH
  [11]Prager, W., Schwaiger, J.: Stability of the multi-Jensen equation. Bull. Korean Math. Soc., 45(1), 133-42 (2008)CrossRef MathSciNet MATH
  
• 作者单位：Pei Sheng Ji (1)
  Shu Juan Zhou (1)
  Hai Yan Xue (1)
  
  1. College of Mathematics, Qingdao University, Qingdao, 266071, P. R. China
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Chinese Library of Science
  
• 出版者：Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society, co-published
• ISSN：1439-7617

文摘

In this paper, we obtain the general solution and stability of the Jensen-cubic functional equation \(f\left( {\frac{{{x_1} + {x_2}}}{2},{\kern 1pt} 2{y_1} + {y_2}} \right) + f\left( {\frac{{{x_1} + {x_2}}}{2},{\kern 1pt} 2{y_1} - {y_2}} \right)\) = f(x ₁, y ₁+y ₂)+f(x ₁, y ₁?em class="EmphasisTypeItalic ">y ₂)+6f(x ₁, y ₁)+f(x ₂, y ₁+y ₂) + f(x ₂, y ₁?em class="EmphasisTypeItalic ">y ₂) + 6f(x ₂, y ₁). Keywords Hyers–Ulam stability mixed cubic-quadric function Jensen-cubic functional equation