The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
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ORTHOGONAL STABILITY OF AN EULER-LAGRANGE-JENSEN (a, b)-CUBIC FUNCTIONAL EQUATION

  • Pasupathi, Narasimman (Department of Mathematics, Thiruvalluvar University College of Arts and Science) ;
  • Rassias, John Michael (Pedagogical Department E.E., Section of Mathematics and Informatics, National and Capodistrian University of Athens) ;
  • Lee, Jung Rye (Department of Data Science, Daejin University) ;
  • Shim, Eun Hwa (Department of Mathematics, Hanyang University)
  • Received : 2022.04.09
  • Accepted : 2022.04.28
  • Published : 2022.05.31
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Abstract

In this paper, we introduce a new generalized (a, b)-cubic Euler-Lagrange-Jensen functional equation and obtain its general solution. Furthermore, we prove the Hyers-Ulam stability of the new generalized (a, b)-cubic Euler-Lagrange-Jensen functional equation in orthogonality normed spaces.

Keywords

Acknowledgement

E. H. Shim was partially supported by the Hanyang University Postdoctoral Research Fund (HY202100000000785).

References

  1. I. Chang, Y. Lee & J. Roh: Nearly general septic functional equation. J. Funct. Spaces 2021 (2021), Art. ID 5643145.
  2. Y. Ding & Y.Z. Xu: Approximate solution of generalized inhomogeneous radical quadratic functional equations in 2-Banach spaces. J. Inequal. Appl. 2019 (2019), Paper No. 31.
  3. F. Drljevic: On a functional which is quadratic on A-orthogonal vectors. Publ. Inst. Math. (Beograd) 54 (1986), 63-71.
  4. M. Fochi: Functional equations in A-orthogonal vectors. Aequationes Math. 38 (1989), 28-40. https://doi.org/10.1007/BF01839491
  5. P. Gavruta: A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings. J. Math. Anal. Appl. 184 (1994), 431-436. https://doi.org/10.1006/jmaa.1994.1211
  6. R. Ger & J. Sikorska: Stability of the orthogonal additivity. Bull. Polish Acad. Sci. Math. 43 (1995), 143-151.
  7. V. Govindan, C. Park, S. Pinelas & S. Baskaran: Solution of a 3-D cubic functional equation and its stability. AIMS Math. 5 (2020), 1693-1705. https://doi.org/10.3934/math.2020114
  8. D.H. Hyers: On the stability of the linear functional equation. Proc. Natl. Acad. Sci. 27 (1941), 222-224. https://doi.org/10.1073/pnas.27.4.222
  9. K. Jun & H. Kim: On the stability of Euler-Lagrange type cubic mappings in quasi-Banach spaces. J. Math. Anal. Appl. 332 (2007), 1335-1350. https://doi.org/10.1016/j.jmaa.2006.11.024
  10. S. Jung, D. Popa & M.T. Rassias: On the stability of the linear functional equation in a single variable on complete metric spaces. J. Global Optim. 59 (2014), 13-16.
  11. Y. Lee, S. Jung & M.T. Rassias: Uniqueness theorems on functional inequalities concerning cubic-quadratic-additive equation. J. Math. Inequal. 12 (2018), 43-61.
  12. C. Park & A. Bodaghi: Two multi-cubic functional equations and some results on the stability in modular spaces. J. Inequal. Appl. 2020 (2020), Paper No. 6.
  13. J.M. Rassias: On approximately of approximately linear mappings by linear mappings. J. Funct. Anal. 46 (1982), 126-130. https://doi.org/10.1016/0022-1236(82)90048-9
  14. J.M. Rassias: On the stability of the Euler-Lagrange functional equation. Chinese J. Math. 20 (1992), 185-190.
  15. J.M. Rassias: Solution of the Ulam stability problem for Euler-Lagrange quadratic mappings. J. Math. Anal. Appl. 220 (1998), 613-639. https://doi.org/10.1006/jmaa.1997.5856
  16. Th.M. Rassias: On the stability of the linear mapping in Banach spaces. Proc. Am. Math. Soc. 72 (1978), 297-300. https://doi.org/10.1090/S0002-9939-1978-0507327-1
  17. K. Ravi, M. Arunkumar & J.M. Rassias: On the Ulam stability for the orthogonally general Euler-Lagrange type functional equation. Int. J. Math. Sci. 3 (2008), no. 8, 36-47.
  18. G. Szabo: Sesquilinear-orthogonally quadratic mappings. Aequationes Math. 40 (1990), 190-200. https://doi.org/10.1007/BF02112295
  19. K. Tamilvanan, N. Alessa, K. Loganathan, G. Balasubramanian & N. Namgyel: General solution and satbility of additive-quadratic functional equation in IRN-space. J. Funct. Spaces 2021 (2021), Art. ID 8019135.
  20. S.M. Ulam: A Colloection of the Mathematical Problems. Interscience Publ., New York, 1960.