Generalized Hyers-Ulam Stability of a Sextic Functional Equation in Paranormed Spaces

K. Ravi; S. Sabarinathan

doi:https://doi.org/10.14445/22315373/IJMTT-V9P506

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 9 | Number 1 | Year 2014 | Article Id. IJMTT-V9P506 | DOI : https://doi.org/10.14445/22315373/IJMTT-V9P506

Generalized Hyers-Ulam Stability of a Sextic Functional Equation in Paranormed Spaces

K. Ravi , S. Sabarinathan

Abstract

In this paper, we obtain the general solution and prove the generalized Hyers-Ulam stability of a new sextic functional equation in paranormed spaces. We also present a counter-example for singular case.

Keywords

Paranormed Spaces, Sextic functional equation, Hyers-Ulam Stability

References

[1] H. Fast, Sur la convergence statistique, Colloq. Math. 2 (1951), 241-244.
[2] J. A. Fridy, On statistical convergence, Analysis 5 (1985), 301-313.
[3] D.H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U.S.A. 27 (1941), 222-224.
[4] S. Karakus, Statistical convergence on probabilistic normed spaces, Math. Commun. 12 (2007), 11-23.
[5] E. Kolk, The statistical convergence in Banach spaces, Tartu Ul. Toime. 928, (1991), 41-52.
[6] M. Mursaleen, -statistical convergence, Math. Slovaca 50 (2000), 111-115.
[7] M. Mursaleen and S.A. Mohiuddine, On lacunary statistical convergence with respect to the intuitionistic fuzzy normed space, J. Computat. Anal. Math. 233 (2009), 142-149.
[8] Ch. Park and D.Y. Shin, Functional equations in paranormed spaces, Adv. differences equations, 2012, 2012:123 (23 pages).
[9] Ch. Park, Stability of an AQCQ-functional equation in paranormed space, Adv. differences equations, 2012, 2012:148 (19 pages).
[10] J.M. Rassias, On approximation of approximately linear mappings by linear mappings, J. Funct. Anal. 46 (1982), 126-130.
[11] K. Ravi, J.M. Rassias and B.V. Senthil Kumar, Stability of reciprocal difference and adjoint functional equations in paranormed spaces: Direct and fixed point methods, Functional Analysis, Approximation and Computation, 5(1), (2013), 57-72.
[12] T. Salat, On the statistically convergent sequences of real numbers, Math. Slovaca 30 (1980), 139-150.
[13] H. Steinhaus, Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math. 2 (1951), 73-34.
[14] Th.M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300.
[15] S.M. Ulam, A collection of mathematical problems, Interscience Publishers, Inc. New York, 1960.
[16] A. Wilansky, Modern Methods in T0pological vector space, McGraw-Hill International Book Co., New York (1978).

Citation :

K. Ravi , S. Sabarinathan, "Generalized Hyers-Ulam Stability of a Sextic Functional Equation in Paranormed Spaces," International Journal of Mathematics Trends and Technology (IJMTT), vol. 9, no. 1, pp. 61-69, 2014. Crossref, https://doi.org/10.14445/22315373/IJMTT-V9P506