Keywords:-
Keywords:
Additive functional equation, Quadratic functional equation, fixed point theory
Article Content:-
Abstract
In this paper authors investigate the general solution of the functional of the for f(3x+9y+27z) +f (3x-9y+27z) +f (3x+9y-27z) + f(-3x+9y+27z) = 3[f(x)- f(-x) +27[f(z)-f(-z)] +18[f(x)+f(-x)] +162[f(y)+ f(-y)] +1458[f(z)+ f(-z)] in Banach space using direct and fixed point methods and also odd and even case discussed the
above functional equation.
2010 Mathematics Subject Classification: 39B52, 32B72, 32B82
References:-
References
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2. T. Aoki, on the stability of the linear transformation in Banach Spaces, J. Math. Soc. Japan, 2 (1950), 64-66.
3. M. Arunkumar, P. Agilan, C. Devi Shyamala Mary, Permanence of a Generalized AQ Functional Equation In Quasi-Beta
Normed Spaces, International Journal of pure and applied Mathematics(Accepted).
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. R. Badora, on approximate derivations, Math. Inequal. Appl. 9 (2006), no.1, 167-173.
6. C. Borelli, G.L. Forti, on a general Hyers-Ulam stability , Internet J. Math. Math. Sci, 18 (1995), 229-236.
7. L. Brown and G. Pedersen, C -algebras, of real rank zero, J. Funct. Analysis, 99, (1991), 138-149.
8. I.S. Chang, E.H. Lee, H.M. Kim, On the Hyers-Ulam-Rassias stability of quadratic functional equations, Math. Ineq. Appl.,
6(1) (2003), 87-95.
9. P.W. Cholewa, Remarks on the stability of functional equations, Aequationes Math., 27 (1984), 76-86.
10. S. Czerwik, on the stability of the quadratic mappings in normed spaces, Abh. Mth. Sem. Univ Hamburg., 62 (1992),59-64.
11. S. Czerwik, Functional Equations and Inequalities in Several Variables, World Scientific, River Edge, NJ, 2002.
12. M. EshaghiGordji, H. Khodaie, Solution and stability of generalized mixed type cubic, quadratic and additive functional
equation in Quasi-Banach spaces, arxiv:0812.2939v1 Math FA, 15 Dec 2008.
13. M. EshaghiGordji, H. Khodaie, J.M. Rassias, Fixed point methods for the stability of general quadratic functional equation,
Fixed Point Theory, 12 (2011), no. 1, 71-82.
14. P. Gavruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl.,
184 (1994), 431-436.
15. K.W. Jun and D.W. Park, Almost derivations on the Banachalgebra Cn0,1 , Bull. Korean Math. Soc. Vol 33, No.3
(1996), 359-366.
16. K.W. Jun, H.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.
17. K.W. Jun, H.M. Kim, on the stability of an n-dimensional quadratic and additive type functional equation, Math. Ineq. Appl
9 (1) (2006), 153-165.
18. Pl. Kannappan, Quadratic functional equation and inner product spaces, Results Math., 27 (1995), 368-372.
19. Pl. Kannappan, Functional Equations and Inequalities with Applications, Springer Monographs in Mathematics, 2009.
20. Matina J. 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), Vol.14 No.
1-2 ,(2014), 22-46.
21. 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 (IJAM),Vol.26. No. 2 (2013),123-136.
22. A. Najati and M.B. Moghimi, On the stability of a quadratic and additive functional equation, J. Math. Aanl.Appl., 337
(2008), 399-415.
23. K. Ravi, M. Arunkumar and J.M. Rassias, On the Ulamstability for the orthogonally general Euler-Lagrange type functional
equation, International Journal of Mathematics Sciences,2008 Vol.3, No. 08, 36-47.
24. S.M. Ulam, Problems in Modern Mathematics, Science Editions, Wiley, New York, 1964.
25. G. ZamaniEskandani, stability of a mixed additive and quadratic functional equation in non-Archimedean Banach modules,
Taiwanese journal of mathematics, Vol.14, No.4,pp. 1309-1324 August 2010.
2. T. Aoki, on the stability of the linear transformation in Banach Spaces, J. Math. Soc. Japan, 2 (1950), 64-66.
3. M. Arunkumar, P. Agilan, C. Devi Shyamala Mary, Permanence of a Generalized AQ Functional Equation In Quasi-Beta
Normed Spaces, International Journal of pure and applied Mathematics(Accepted).
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. R. Badora, on approximate derivations, Math. Inequal. Appl. 9 (2006), no.1, 167-173.
6. C. Borelli, G.L. Forti, on a general Hyers-Ulam stability , Internet J. Math. Math. Sci, 18 (1995), 229-236.
7. L. Brown and G. Pedersen, C -algebras, of real rank zero, J. Funct. Analysis, 99, (1991), 138-149.
8. I.S. Chang, E.H. Lee, H.M. Kim, On the Hyers-Ulam-Rassias stability of quadratic functional equations, Math. Ineq. Appl.,
6(1) (2003), 87-95.
9. P.W. Cholewa, Remarks on the stability of functional equations, Aequationes Math., 27 (1984), 76-86.
10. S. Czerwik, on the stability of the quadratic mappings in normed spaces, Abh. Mth. Sem. Univ Hamburg., 62 (1992),59-64.
11. S. Czerwik, Functional Equations and Inequalities in Several Variables, World Scientific, River Edge, NJ, 2002.
12. M. EshaghiGordji, H. Khodaie, Solution and stability of generalized mixed type cubic, quadratic and additive functional
equation in Quasi-Banach spaces, arxiv:0812.2939v1 Math FA, 15 Dec 2008.
13. M. EshaghiGordji, H. Khodaie, J.M. Rassias, Fixed point methods for the stability of general quadratic functional equation,
Fixed Point Theory, 12 (2011), no. 1, 71-82.
14. P. Gavruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl.,
184 (1994), 431-436.
15. K.W. Jun and D.W. Park, Almost derivations on the Banachalgebra Cn0,1 , Bull. Korean Math. Soc. Vol 33, No.3
(1996), 359-366.
16. K.W. Jun, H.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.
17. K.W. Jun, H.M. Kim, on the stability of an n-dimensional quadratic and additive type functional equation, Math. Ineq. Appl
9 (1) (2006), 153-165.
18. Pl. Kannappan, Quadratic functional equation and inner product spaces, Results Math., 27 (1995), 368-372.
19. Pl. Kannappan, Functional Equations and Inequalities with Applications, Springer Monographs in Mathematics, 2009.
20. Matina J. 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), Vol.14 No.
1-2 ,(2014), 22-46.
21. 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 (IJAM),Vol.26. No. 2 (2013),123-136.
22. A. Najati and M.B. Moghimi, On the stability of a quadratic and additive functional equation, J. Math. Aanl.Appl., 337
(2008), 399-415.
23. K. Ravi, M. Arunkumar and J.M. Rassias, On the Ulamstability for the orthogonally general Euler-Lagrange type functional
equation, International Journal of Mathematics Sciences,2008 Vol.3, No. 08, 36-47.
24. S.M. Ulam, Problems in Modern Mathematics, Science Editions, Wiley, New York, 1964.
25. G. ZamaniEskandani, stability of a mixed additive and quadratic functional equation in non-Archimedean Banach modules,
Taiwanese journal of mathematics, Vol.14, No.4,pp. 1309-1324 August 2010.
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Govindan, V., Murthy, S., & Kokila, G. (2018). Hyers-Ulam Stability of AQ Functional Equation. International Journal Of Mathematics And Computer Research, 6(01), 1852-1859. https://doi.org/10.31142/ijmcr.v6i01.2