ORTHOGONAL STABILITY OF A MIXED TYPE ADDITIVE AND QUADRATIC FUNCTIONAL EQUATION

[1] T. Aoki, On the stability ofthe linear transformation in Banach spaces,
J. Math. Soc. Japan, 2 (1950), 64-66.
198
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
K.Ravi, John Michael Rassias and R.Murali
P.W. Cholewa, Remarks on the stability of functional equations , Ae-quationes Math., 27 (1984), 76-86.
S. Czerwik, On the stability of the quadratic mappings in normed spaces, Abh. Math. Sem. Univ Hamburg., 62 (1992), 59-64.
F. Drljevic, On a functional which is quadratic on A-orthogonal vectors, Publ. Inst. Math. (Beograd) 54, (1986),63-71.
Fridoum Moradlou, Hamid Vaezi, G. Zamani Eskandani, Hyers-
Ulam-Rassiass Stability of a quadratic and additive functional equation in quasi- Banach spaces,Mediterr.J.Math. 6, (2009), 233-248.
P. Gavruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl., 184 (1994), 431¬436.
R. Ger and J. Sikorska, Stability of the orthogonal additivity, Bull.
Polish Acad. Sci. Math. 43, (1995), 143-151.
S. Gudder and D. Strawther, Orthogonally additive and orthogonally increasing functions on vector spaces, Pacific J. Math. 58, 1995, 427-436.
D.H. Hyers, On the stability of the linear functional equation, Proc.
Nat. Acad. Sci., U.S.A., 27 (1941) 222-224.
M.S. Moslehian, On the orthogonal stability of the Pexiderized quadratic equation, J. Differ. Equations Appl. 11, No. 11, (2005), 999¬1004.
M.S. Moslehian, On the stability ofthe orthogonal Pexiderized Cauchy
equation, J. Math. Anal. Appl. 318, No. 1, (2006), 211-223.
C. Park, On the stability of the orthogonally quartic functional equa¬tions, Bull. Iranian Math. Soc. 31 (1), (2005), 63-70.
J.M. Rassias, On approximately of approximately linear mappings by linear mappings, J. Funct. Anal. USA, 46 (1982) 126-130.
J.M. Rassias, On approximately of approximately linear mappings by
linear mappings, Bull. Sc. Math, 108 (1984), 445-446.
Th.M. Rassias, On the stability ofthe linear mapping in Banach spaces,
Proc.Amer.Math. Soc., 72 (1978), 297-300.
Th.M. Rassias, On the stability of functional equations in Banach
spaces, J. Math. Anal. Appl. 251, (2000), 264-284.
Orthogonal Stability of an Additive and Quadratic Functional Equation 199 [17] J. Ratz, On orthogonally additive mappings, Aequationes Math. 28,
(1985), 35-49.
[18] K. Ravi and M. Arunkumar, On the Ulam- Gavruta- Rassias stability of the orthogonally Euler- Lagrange type functional equation, IJAMAS,
7, No. Fe 07, (2007), 143-156.
[19] K. Ravi, M. Arunkumar and J.M. Rassias, Ulam stability for the orthogonally general Euler- Lagrange type functional equation, IJMS, 3,
No.8, (2008), 36-47.
[20] F. Skof, Proprieta locali e approssimazione di operatori, Rend. Sem.
Mat. Fis. Milano 53, (1983), 113-129.
[21] S.M. Ulam, Problems in Modern Mathematics, Rend. Chap.VI,Wiley,
New York, 1960.
[22] F. Vajzovic, Uber das Funktional H mit der Eigenschaft: (x,y) = 0 == H(x + y) + H(x - y) = 2H(x) + 2H(y),Glasnik Mat. Ser. III 2 (22),
(1967), 73-81.