Korean J. Math.  Vol 26, No 4 (2018)  pp.615-628
DOI: https://doi.org/10.11568/kjm.2018.26.4.615

Stability of trigintic functional equation in multi-Banach spaces: fixed point approach

Murali Ramdoss, Antony Raj Aruldass, Choonkil Park, Siriluk Paokanta


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.


Hyers-Ulam stability; multi-Banach space; trigintic functional equation; fixed point method

Subject classification

39B62; 47H10; 39B52; 39A11


National research Foundation of Korea

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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. (Google Scholar)

T. Aoki, On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan. 2 (1950), 64--66. (Google Scholar)

H. Azadi Kenary, Direct method and approximation of the reciprocal difference functional equations in various normed spaces, An. c{S}tiinc{t}. Univ. Al. I. Cuza Iac{s}i. Mat. (N.S.) 63 (2017), 245--263. (Google Scholar)

J. Brzc{e}dk, 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. (Google Scholar)

H.G. Dales, M.S. Moslehian, Stability of mappings on multi-normed spaces, Glasgow Math. J. 49 (2007), 321--332. (Google Scholar)

D.H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U.S.A. 27 (1941), 222--224. (Google Scholar)

D.H. Hyers, G. Isac, Th.M. Rassias, Stability of Functional Equations in Several Variables, Birkh"{a}user, Basel, 1998. (Google Scholar)

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. (Google Scholar)

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. (Google Scholar)

V. Radu, The fixed point alternative and the stability of functional equations, Fixed Point Theory 4 (2003), 91--96. (Google Scholar)

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. (Google Scholar)

Th.M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Am. Math. Soc. 72 (1978), 297--300. (Google Scholar)

S.M. Ulam, A Collection of the Mathematical Problems, Interscience, New York, 1960. (Google Scholar)

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). (Google Scholar)

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. (Google Scholar)

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). (Google Scholar)

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. (Google Scholar)


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