참고문헌
- J. Aczel and J. Dhombres, Functional Equations in Several Variables, With applications to mathematics, information theory and to the natural and social sciences. Encyclopedia of Mathematics and its Applications, 31. Cambridge University Press, Cambridge, 1989
- D. Amir, Characterizations of inner product spaces, Operator Theory: Advances and Applications, 20. Birkhauser Verlag, Basel, 1986
- Y. Benyamini and J. Lindenstrauss, Geometric Nonlinear Functional Analysis. Vol. 1, American Mathematical Society Colloquium Publications, 48. American Mathematical Society, Providence, RI, 2000
- P. W. Cholewa, Remarks on the stability of functional equations, Aequationes Math. 27 (1984), no. 1-2, 76-86 https://doi.org/10.1007/BF02192660
- S. Czerwik, On the stability of the quadratic mapping in normed spaces, Abh. Math. Sem. Univ. Hamburg 62 (1992), 59-64 https://doi.org/10.1007/BF02941618
- P. Gavruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl. 184 (1994), no. 3, 431-436 https://doi.org/10.1006/jmaa.1994.1211
- A. Grabiec, The generalized Hyers-Ulam stability of a class of functional equations, Publ. Math. Debrecen 48 (1996), no. 3-4, 217-235
- D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U. S. A. 27 (1941), 222-224
- P. Jordan and J. von Neumann, On inner products in linear, metric spaces, Ann. of Math. (2) 36 (1935), no. 3, 719-723 https://doi.org/10.2307/1968653
- K. Jun and Y. Lee, On the Hyers-Ulam-Rassias stability of a Pexiderized quadratic inequality, Math. Inequal. Appl. 4 (2001), no. 1, 93-118
- Pl. Kannappan, Quadratic functional equation and inner product spaces, Results Math. 27 (1995), no. 3-4, 368-372 https://doi.org/10.1007/BF03322841
- A. Najati and M. B. Moghimi, Stability of a functional equation deriving from quadratic and additive functions in quasi-Banach spaces, J. Math. Anal. Appl. 337 (2008), no. 1, 399-415 https://doi.org/10.1016/j.jmaa.2007.03.104
- Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), no. 2, 297-300
- S. Rolewicz, Metric Linear Spaces, PWN?Polish Scientific Publishers, Warsaw; D. Reidel Publishing Co., Dordrecht, 1984
- F. Skof, Local properties and approximation of operators, Rend. Sem. Mat. Fis. Milano 53 (1983), 113-129 https://doi.org/10.1007/BF02924890
- S. M. Ulam, A Collection of Mathematical Problems, Interscience Tracts in Pure and Applied Mathematics, no. 8 Interscience Publishers, New York-London, 1960
피인용 문헌
- Homomorphisms in quasi-Banach algebras associated with a Pexiderized Cauchy-Jensen functional equation vol.25, pp.9, 2009, https://doi.org/10.1007/s10114-009-7648-z
- On Approximate Additive–Quartic and Quadratic–Cubic Functional Equations in Two Variables on Abelian Groups vol.58, pp.1-2, 2010, https://doi.org/10.1007/s00025-010-0018-4
- Approximate Behavior of Bi-Quadratic Mappings in Quasinormed Spaces vol.2010, pp.1, 2010, https://doi.org/10.1155/2010/472721
- Generalized Stability of Euler-Lagrange Quadratic Functional Equation vol.2012, 2012, https://doi.org/10.1155/2012/219435
- On the stability of a functional equation deriving from additive and quadratic functions vol.2012, pp.1, 2012, https://doi.org/10.1186/1687-1847-2012-98
- Approximate Cauchy functional inequality in quasi-Banach spaces vol.2011, pp.1, 2011, https://doi.org/10.1186/1029-242X-2011-102