On the Ulam stability of the Cauchy-Jensen equation and the additive-quadratic equation

Volume 8, Issue 5, pp 710--718 http://dx.doi.org/10.22436/jnsa.008.05.23

Download PDF

Download XML

• Export citations
  • CITATIONS & REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • ARTICLE CITATION
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)

• 1371 Downloads
• 2164 Views

Authors

Jae-Hyeong Bae - Humanitas College, Kyung Hee University, Yongin 446-701, Republic of Korea. Won-Gil Park - Department of Mathematics Education, College of Education, Mokwon University, Daejeon 302-729, Republic of Korea.

Abstract

In this paper, we investigate the Ulam stability of the functional equations \[2f ( x + y; \frac{z + w}{ 2} ) = f(x; z) + f(x;w) + f(y; z) + f(y;w)\] and \[f(x + y; z + w) + f(x + y; z - w) = 2f(x; z) + 2f(x;w) + 2f(y; z) + 2f(y;w)\] in paranormed spaces.

Share and Cite

Keywords

• Cauchy-Jensen mapping
• additive-quadratic mapping
• paranormed space.

MSC

•  39B52
•  39B82

References

• [1] Y. J. Cho, C. Park, Y. O. Yang, Stability of derivations in fuzzy normed algebras, J. Nonlinear Sci. Appl., 8 (2015), 1-7.


• [2] P. Găvruţa, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl., 184 (1994), 431-436.


• [3] D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci., 27 (1941), 222-224.


• [4] C. Park, Additive \(\rho\)-functional inequalities, J. Nonlinear Sci. Appl., 7 (2014), 296-310.


• [5] C. Park, J. R. Lee, Functional equations and inequalities in paranormed spaces, J. Inequal. Appl., 2013 (2013), 23 pages.


• [6] C. Park, J. R. Lee, Approximate ternary quadratic derivation on ternary Banach algebras and C*-ternary rings: revisited, J. Nonlinear Sci. Appl., 8 (2015), 218-223.


• [7] W. G. Park, J. H. Bae, On a Cauchy-Jensen functional equation and its stability, J. Math. Anal. Appl., 323 (2006), 634-643.


• [8] W. G. Park, J. H. Bae, B. H. Chung, On an additive-quadratic functional equation and its stability, J. Appl. Math. & Computing, 18 (2005), 563-572.


• [9] T. M. Rassias, On the stability of linear mappings in Banach spaces, Proc. Amer. Math. Soc., 72 (1978), 297-300.


• [10] S. M. Ulam, A Collection of Mathematical Problems, Interscience Publishers, New York (1960)


• [11] A. Wilansky, Modern Methods in Topological Vector Space, McGraw-Hill International Book Co., New York (1978)