Volume 33 | Number 1 | Year 2016 | Article Id. IJMTT-V33P507 | DOI : https://doi.org/10.14445/22315373/IJMTT-V33P507
In this paper, the authors established the solution and generalized Ulam - Hyers stability of the additive-quartic functional equation in Quasi Banach spaces.
[1] J.Aczel and Dhombres J., Functional Equations in Several Variables, Cambridge Univ, Press, 1989.
[2] T.Aoki , On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan, 2 (1950), 64-66.
[3] M.Arunkumar.,J.M.Rassias., On the generalized Ulam- Hyers stability of an AQ-mixed type functional equation with counter examples, Far East Journal of Applied Mathematics, Volume 71, No. 2, (2012), 279-305.
[4] M. Arunkumar.,P.Agilan., 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] M.Arunkumar., P.Agilan., 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] P.Gavruta ., A generalizationof the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl., 184 (1994), 431-436.
[9] M. Eshaghi Gordji., N.Ghobadipour .,J.M. Rassias ., Fuzzy stability of additive quadratic functionalEquations, arXiv:0903.0842v1 [math.FA] 4 Mar 2009.
[10] O.Hadzic ., Fixed Point Theory in Probabilistic Metric Spaces, vol. 536 of Mathematics and its Applications, Kluwer Academic, Dordrecht, The Netherlands, 2001.
[11] O.Pap E Pap . 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] D.H.Hyers., On the stability of the linear functional equation, Proc. Nat. Acad.Sci.,U.S.A., 27, (1941), 222-224.
[13] D.H.Hyers .,G. Isac., Th.M.Rassias ., Stability of unctional equations in several variables, Birkhauser, Basel, 1998.
[14] H.M..Jun.. M.Kim., 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] S.M.Jung., Hyers-Ulam-Rassias Stability of Functional Equations in Mathematical Analysis, Hadronic Press, Palm Harbor, 2001.
[16] S.H.Lee., S.M.Im ., I.S.Hwang., Quartic functional equations, J. Math. Anal. Appl., 307, (2005), 387-394. [17] P.L.Kannappanl., Functional Equations and Inequalities with Applications, Springer Monographs in Mathematics, 2009.
[18] S.Murthy.,M.Arunkumar., G.Ganapathy., P. Rajarethinam ., 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] A.Najati., M.B.Moghimi ., On the Stability of a quadratic and additive functional equation, J. Math. Anal. Appl. 337 (2008), 399-415.
[20] C.Park., Orthogonal Stability of an Additive-Quadratic Functional Equation, Fixed Point Theory and Applications 2001 2011:66.
[21] J.M.Rassias., M Arunkumar ., S.Ramamoorthi., 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] J.M.Rassias., On approximately of approximately linear mappings by linear mappings, J. Funct. Anal. USA, 46, (1982) 126-130.
[23] Th.M.Rassias., On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72 (1978), 297- 300.
[24] Th.M.,Rassias., Functional Equations, Inequalities and Applications, Kluwer Acedamic Publishers, Dordrecht, Bostan London, 2003.
[25] K.Ravi., M.Arunkumar. and Rassias J. M., On the Ulam stability for the orthogonally general Euler-Lagrange type functional equation, International Journal of Mathematical Sciences, Autumn 2008 Vol.3, No. 08, 36-47.
[26] B. schweizer and A. Sklar, Probabilistic Metric Spaces, North-Holland Series in Probability and Applied Mathematics, North-Holland Publishing, New York, NY, USA, 1983.
[27] A.N.Sherstnev ., On the notion of a random normed space, Doklady Akademii Nauk SSSR, vol. 149, (1963) 280-283, (Russian).
[28] S.M.Ulam., Problems in Modern Mathematics, Science Editions, Wiley, New York, 1964.
[29] G.Zamani Eskandani., Hamid Vaezi, Y.N.Dehghan ., Stability of A Mixed Additive and Quadratic Functional Equation In Non-Archimedean Banach Modules, Taiwanese Journal of Mathematics, Vol. 14, No. 4, (2010), 1309-1324.
P.Srikanth Rao, Veena Kulkarni, "Additive-Quartic Functional Equations are Stable in Quasi-Banach Spaces," International Journal of Mathematics Trends and Technology (IJMTT), vol. 33, no. 1, pp. 35-41, 2016. Crossref, https://doi.org/10.14445/22315373/IJMTT-V33P507