International Journal of Mathematics Trends and Technology
Volume 32 | Number 2 | Year 2016 | Article Id. IJMTT-V32P512 | DOI : https://doi.org/10.14445/22315373/IJMTT-V32P512
In this paper, the authors established the solution and generalized Ulam - Hyers stability of the additive-quartic functional equation in Quasi Banach spaces.
[1] Aczel J. and Dhombres J., Functional Equations in Several Variables, Cambridge Univ, Press, 1989.
[2] Aoki T., On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan, 2 (1950), 64-66.
[3] Arunkumar M., Rassias John M., On the generalized Ulam-Hyers stability of an AQmixed type functional equation with counter examples, Far East Journal of Applied Mathematics, Volume 71, No. 2, (2012), 279-305.
[4] Arunkumar M., Agilan P., Additive Quadratic functional equation are stable in Banach space: A Fixed Point Approach, International Journal of pure and Applied Mathematics, Vol. 86 No.6, 951-963, (2013).
[5] Arunkumar M., Agilan P., Additive Quadratic functional equation are stable in Banach space: A Direct Method, Far East Journal of Mathematical Sciences, Volume 80, No. 1, (2013), 105 – 121.
[6] S. S. Chang, Y. J. Cho, and S. M. Kang, Nonlinear Operator Theory in Probabilistic Metric Spaces, Nova Science Publishers, Huntington, NY, USA, 2001.
[7] Czerwik S., Functional Equations and Inequalities in Several Variables, World Scientific, River Edge, NJ, 2002.
[8] Gavruta P., A generalizationof the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl., 184 (1994), 431-436.
[9] Eshaghi Gordji M., Ghobadipour N., Rassias J. M., Fuzzy stability of additive quadratic functional Equations, arXiv:0903.0842v1 [math.FA] 4 Mar 2009.
[10] Hadzic O., Pap E., Fixed Point Theory in Probabilistic Metric Spaces, vol. 536 of Mathematics and its Applications, Kluwer Academic, Dordrecht, The Netherlands, 2001.
[11] Hadzic O., Pap E. and Budincevic M., Countable extension of triangular norms and their applications to the fixed point theory in probabilistic metric spaces, Kybernetika, vol. 38, no. 3, (2002) 363-382.
[12] Hyers D. H., On the stability of the linear functional equation, Proc. Nat. Acad.Sci.,U.S.A., 27, (1941), 222-224.
[13] Hyers D. H., Isac G., Rassias Th. M., Stability of unctional equations in several variables, Birkhauser, Basel, 1998.
[14] Jun K. W., Kim H. M., On the Hyers-Ulam-Rassias stability of a generalized quadratic and additive type functional equation, Bull. Korean Math. Soc. 42(1), (2005), 133-148.
[15] Jung S. M., Hyers-Ulam-Rassias Stability of Functional Equations in Mathematical Analysis, Hadronic Press, Palm Harbor, 2001.
[16] Lee S.H., Im S.M., Hwang I.S., Quartic functional equations, J. Math. Anal. Appl., 307, (2005), 387-394.
[17] Kannappan Pl., Functional Equations and Inequalities with Applications, Springer Monographs in Mathematics, 2009.
[18] Murthy S., Arunkumar M., Ganapathy G., Rajarethinam P., Stability of mixed type additive quadratic functional equation in Random Normed space, International Journal of Applied Mathematics Vol. 26. No. 2 (2013), 123-136.
[19] Najati A., Moghimi M. B., On the Stability of a quadratic and additive functional equation, J. Math. Anal. Appl. 337 (2008), 399-415.
[20] Park C., Orthogonal Stability of an Additive-Quadratic Functional Equation, Fixed Point Theory and Applications 2001 2011:66.
[21] Rassias M. J., Arunkumar M., Ramamoorthi S., Stability of the Leibniz additive-quadratic functional equation in Quasi-Beta normed space: Direct and fixed point methods, Journal of Concrete and Applicable Mathematics (JCAAM), (Accepted).
[22] Ulam S. M., Problems in Modern Mathematics, Science Editions, Wiley, New York, 1964.
R. Kodandan, R. Bhuvanavijaya, "Additive – Quartic Functional Equations are Stable in Quasi-Banach Space," International Journal of Mathematics Trends and Technology (IJMTT), vol. 32, no. 2, pp. 71-78, 2016. Crossref, https://doi.org/10.14445/22315373/IJMTT-V32P512
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