Stability of n-type Cubic Functional Equation in Non- Archimedean Normed space: using direct and fixed point methods

	International Journal of Mathematics Trends and Technology (IJMTT)
	© 2016 by IJMTT Journal
	Volume-32 Number-2
	Year of Publication : 2016
	Authors : V. Govindan, S. Murthy, M. Arunkumar
	10.14445/22315373/IJMTT-V32P514

V. Govindan S. Murthy, M. Arunkumar "Stability of n-type Cubic Functional Equation in Non- Archimedean Normed space: using direct and fixed point methods", International Journal of Mathematics Trends and Technology (IJMTT). V32(2):87-96 April 2016. ISSN:2231-5373. www.ijmttjournal.org. Published by Seventh Sense Research Group.

Abstract
In this paper, the authors established the Stability for n- type of Cubic functional equation of the form in Non-Archimedean Normed spaces,using direct and fixed point methods ,where n is a positive integer with n>0.

References
[1] J.Aczel and J.Dhombres, Functtional Equation in several variables, Combridge 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] L.M.Arriola and W.Bayer,the sability of the Cauchy functional equation over p-adic fields,Real Analysis exchange.31(2005/2006),125-132
[4] C. Baak, D. Boo, Th.M. Rassias, Generalized additive mapping in Banach modules and isomorphism between C*-algebras, J. Math. Anal. Appl. 314, (2006), 150-161.
[5]. T.Bag,S.K.Samanta, finite dimensional fuzzy normed linear spaces, J .Fuzzy Math, 11(3) (2003) 687-705.
[6]. T.Bag , S.K.samanta fuzzy bounded linear operations,fuzzy sets and systems, 151 (2005) 513-547.
[7]. C.Borelli, G.L.Forti, on a general Hpers-ulam satability , internal J.Math Sci, 18(1995),229-236.
[8].P.W.Cholewa, Remarks on the stability of funcitional equation, Aequationes math ,27 (1984),76-86.
[9].S.Czerwik, on the stability of the quadratic mapping in normed spaces Abh.Math.sem.univ Hambury,62 (1992),59-64.
[10]. S.Czerwik, functional equation and inequalities in several variables , World scientific, River Edge, NJ,2002.
[11]. P.Gavruta, A generation of the hypers Ulam-Rassias stability of approximately additive mapping, J.Ma th. Anal. Appl. 184, (1994), 431-436.
[12].D.H.Hypers, on the stability of the linear functional equation, proc.nat.Sci.U.S.A., 27 (1941) 222-224.
[13]. D.H.Hypers, G.Isac, Th.M.Rassias, satbility of the functional equation in several variables, Birkhauser , Basel ,1998
[14]. K.W.Jun ,H.M.Kim on satbility of an n-dimensional quadratic and additive tpye functional equation, Math. Ineq.appl. 9(1) (2006),153-165.
[15].S.M.Jung, on the Hypers-Ulam stability of funcitional equation that have the quratic property J.Math anal. Appl, 222(1998), 126-137.
[16].S.M.Jung, on the Hypers-Ulam-Rassias stability of funcitional equation in Mathematical analysis , Hadronic press, plam Harbor, 2001
[17].PI.Kannappan, quadratic functional Equation inner product spaces, results Math ,27, No 3-4,(1995), 368-372.
[18]. PI.Kannappan, Functional Equations and inequalities with application ,Springer monographs in mathematics, 2009.
[19]. M.S.Moslehian and Th.M.Rassias,stability of functional equations in non-Archimedean spaces,applicable Analysis and Discrete Mathematics,1(2007),325-334.
[20] .C.Park,Generlized quadratic mappings in several variables.Nonlinear .Anal.TMA.57(2004),713-722.
[21]. C.Park,Generlized quadratic mappings in Banach modules .J.Math.Anal.Appl.62(2005),no.4,643-654.
[22].J.H.Park, intutionistic fuzzy metric spaces, chaos,solitons and Fractols, 22(2004),1039-1046.
[23].J.M.Rassias ,on approximately linear mappings by linear mapping , J.Funct. Anal, 46, (1982) 126-130.
[24].J.M.Rassias, on approximately of approximately linear mapping by Linear mappings Bull. Sc.Math , 108, (1984), 445- 446.
[25].Th.M.Rassias , on the stability of the linear mapping in babach spaces Proc.Amer.Math.soc, 72(1978),297-300.
[26].Th.M.Rassias, on the stability of the functional equation in banach spaces J.Math .Anal.Appl.251,(2000),254-284.
[27].Th.M.Rassias,functional equations , inequalities and Applications, Kluwer Acedamic publishers, Dordrecht, Bosan London,2003.
[28].K.Ravi, M.Arunkumar and J.M.Rassias, on the ulam stability for orthogonally general Euler-lagrange type functional equation, international journal of mathematical sciences, Autumn 2008 vol 3, no 08,36-47.
[29].K.Ravi, M.Arunkumar and P.Narasimman,fuzzy stability of a additive functional equation, international Journal of mathematical Sciences, vol 9, No All , Autumn 2011, 88-105.
[30].S.M.Ulam, problems in modern Mathematics, science Editions, Wiley, Newyork, 1964(chapter VI, some questions in analysis 1,stability).
[31] S.M.Ulam,A Collection of Mathematical problems,Interscience Tracts Purre and Apllied Mathematics,Interscience publisher,Newyork,1960.
[32] V.S.Vladimirov,I.V.Volovich and E.I.Zelenov,p-adic Analysis and Mathematical Physics.World scientific.1994.

Keywords
Cubic functional equation,Non-Archimedean noemed space,direct and fixed point Stability.