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STABILITY OF TRIGINTIC FUNCTIONAL EQUATION IN MULTI-BANACH SPACES: FIXED POINT APPROACH

  • Ramdoss, Murali (PG and Research Department of Mathematics, Sacred Heart College (Autonomous)) ;
  • Aruldass, Antony Raj (PG and Research Department of Mathematics, Sacred Heart College (Autonomous)) ;
  • Park, Choonkil (Research Institute for Natural Sciences, Hanyang University) ;
  • Paokanta, Siriluk (Research Institute for Natural Sciences, Hanyang University)
  • Received : 2018.07.14
  • Accepted : 2018.11.19
  • Published : 2018.12.30

Abstract

In this paper, we introduce the pioneering trigintic functional equation. Moreover, we establish the general solution of the trigintic functional equation and prove the Hyers-Ulam sum and product stabilities of the same equation in multi-Banach spaces by employing the fixed point approach.

Keywords

References

  1. S. Alizadeh, F. Moradlou, Approximate a quadratic mapping in multi-Banach spaces, A fixed point approach, Int. J. Nonlinear Anal. Appl. 7 (2016), 63-75.
  2. T. Aoki, On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan. 2 (1950), 64-66. https://doi.org/10.2969/jmsj/00210064
  3. H. Azadi Kenary, Direct method and approximation of the reciprocal difference functional equations in various normed spaces, An. Stiint. Univ. Al. I. Cuza Iasi. Mat. (N.S.), 63 (2017), 245-263.
  4. J. Brzedk, W. Fechner, M.S. Moslehian, J. Sikorska, Recent developments of the conditional stability of the homomorphism equation, Banach J. Math. Anal., 9 (2015), 278-326. https://doi.org/10.15352/bjma/09-3-20
  5. H.G. Dales, M.S. Moslehian, Stability of mappings on multi-normed spaces, Glasgow Math. J. 49 (2007), 321-332. https://doi.org/10.1017/S0017089507003552
  6. D.H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U.S.A. 27 (1941), 222-224. https://doi.org/10.1073/pnas.27.4.222
  7. D.H. Hyers, G. Isac, Th.M. Rassias, Stability of Functional Equations in Several Variables, Birkhauser, Basel, 1998.
  8. D. Mihet, V. Radu, On the stability of the additive Cauchy functional equation in random normed spaces, J. Math. Anal. Appl. 343 (2008), 567-572. https://doi.org/10.1016/j.jmaa.2008.01.100
  9. F. Moradlou, Approximate Euler-Lagrange-Jensen type additive mapping in multi-Banach spaces: A fixed point approach, Commun. Korean Math. Soc. 28 (2013), 319-333. https://doi.org/10.4134/CKMS.2013.28.2.319
  10. V. Radu, The fixed point alternative and the stability of functional equations, Fixed Point Theory 4 (2003), 91-96.
  11. J.M. Rassias, R. Murali, M.J. Rassias, A.A. Raj, General solution, stability and non-stability of quattuorvigintic functional equation in multi-Banach spaces, Int. J. Math. Appl. 5 (2017), 181-194.
  12. 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
  13. S.M. Ulam, A Collection of the Mathematical Problems, Interscience, New York, 1960.
  14. L. Wang, B. Liu, R. Bai, Stability of a mixed type functional equation on multi-Banach spaces: A fixed point approach, Fixed Point Theory Appl. 2010, Art. ID 283827 (2010).
  15. X. Wang, L. Chang, G. Liu, Orthogonal stability of mixed additive-quadratic Jensen type functional equation in multi-Banach spaces, Adv. Pure Math. 5 (2015), 325-332. https://doi.org/10.4236/apm.2015.56031
  16. Z. Wang, X. Li, Th.M. Rassias, Stability of an additive-cubic-quartic functional equation in multi-Banach spaces, Abstr. Appl. Anal. 2011, Art. ID 536520 (2011).
  17. T.Z. Xu, J.M. Rassias, W.X. 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.