Stability of Euler-Lagrange-Jensen's (a,b)- Sextic Functional Equation in Multi-Banach Spaces

Main Article Content

John Michael Rassias
R. Murali
A. Antony Raj


In this paper, we prove the Hyers-Ulam Stability of Euler-Lagrange-Jensen's (a,b)-Sextic Functional Equation in Multi-Banach Spaces.

Article Details


  1. T. Aoki, On the stability of the linear transformation in Banach spaces, J.Math. Soc. Japan 2 (1950), 64-66.
  2. Dales, H.G and Moslehian, Stability of mappings on multi-normed spaces, Glasgow Math. J. 49 (2007), 321-332.
  3. Fridoun Moradlou, Approximate Euler-Lagrange-Jensen type Additive mapping in Multi-Banach Spaces: A Fixed point Approach, Commun. Korean Math. Soc. 28 (2013), 319-333.
  4. P. Gavruta, On a problem of G.Isac and Th.M.Rassias concerning the stability of mappings, J. Math. Anal. Appl. 261 (2001), 543-553.
  5. D.H.Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. USA 27 (1941), 222-224.
  6. John Michael Rassias, R. Murali, Matina John Rassias, A. Antony Raj, General Solution, stability and Non-sstability of Quattuorvigintic functional equation in Multi-Banach spaces, Int. J. Math. Appl. 5 (2017), 181-194.
  7. Manoj Kumar and Ashish Kumar, Stability of Jenson Type Quadratic Functional Equations in Multi-Banach Spaces, Int. J. Math. Arch. 3(4) (2012), 1372-1378.
  8. D. Mihet and V. Radu, On the stability of the additive Cauchy functional equation in random normed spaces, J. Math. Anal. Appl. 343 (2008), 567-572.
  9. R. Murali, Matina J. Rassias and V. Vithya, The General Solution and stability of Nonadecic Functional Equation in Matrix Normed Spaces, Malaya J. Mat. 5(2) (2017), 416-427.
  10. V.Radu, The fixed point alternative and the stability of functional equations, Fixed Point Theory 4 (2003), 91-96.
  11. K. Ravi, J.M. Rassias and B.V. Senthil Kumar, Ulam-Hyers stability of undecic functional equation in quasi-beta normed spaces fixed point method, Tbilisi Math. Sci. 9 (2) (2016), 83-103.
  12. K. Ravi, J.M. Rassias, S. Pinelas and S.Suresh, General solution and stability of Quattuordecic functional equation in quasi beta normed spaces, Adv. Pure Math. 6 (2016), 921-941.
  13. J. M. Rassias and M. Eslamian, Fixed points and stability of nonic functional equation in quasi-β-normed spaces, Cont. Anal. Appl. Math. 3 (2) (2015), 293-309.
  14. Th.M. Rassias, On the stability of the linear mappings in Banach Spaces, Proc. Amer. Math. Soc., 72 (1978), 297-300.
  15. Th.M. Rassias, On the stability of functional equations and a problem of Ulam, Acta. Appl. Math. 62 (2000) 23 - 130.
  16. Tian Zhou Xu, John Michael Rassias and Wan Xin Xu, Generalized Ulam - Hyers Stability of a General Mixed AQCQ functional equation in Multi-Banach Spaces: A Fixed point Approach, Eur. J. Pure Appl. Math. 3 (2010), 1032-1047.
  17. S.M. Ulam, A Collection of the Mathematical Problems, Interscience, New York, (1960).
  18. T. Z. Xu, J. M. Rassias, M. J. Rassias and W. X. Xu, A fixed point approach to the stability of quintic and sextic functional equations in quasi-β-normed spaces, J. Inequal. Appl. 2010 (2010), Article ID 423231.
  19. Xiuzhong Wang, Lidan Chang, Guofen Liu, Orthogonal Stability of Mixed Additive-Quadratic Jenson Type Functional Equation in Multi-Banach Spaces, Adv. Pure Math. 5 (2015), 325-332.