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ผ๋ฌธKCI ๋ฑ์ฌ
Quadratic ๐บ-functional inequalities
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In this paper, we solve the quadratic ๐บ-functional inequalities |f(x+y)+f(x-y)-2f(x)-2f(y)| <=๐บ(4 f(frac{x+y}{2}) + f(x-y)- 2f(x) - 2 f(y))| ---(0.1) where ๐บ is a fixed complex number with |๐บ|<1, and |4 f(frac{x+y}{2}) + f(x-y)- 2 f(x) -2 f(y)| <|๐บ(f(x+y)+f(x-y)-2f(x)-2f(y))| --(0.2) where rho isfixed complex number with |๐บ|
Abstract
In this paper, we solve the quadratic ๐บ-functional inequalities |f(x+y)+f(x-y)-2f(x)-2f(y)| <=๐บ(4 f(frac{x+y}{2}) + f(x-y)- 2f(x) - 2 f(y))| ---(0.1) where ๐บ is a fixed complex number with |๐บ|<1, and |4 f(frac{x+y}{2}) + f(x-y)- 2 f(x) -2 f(y)| <|๐บ(f(x+y)+f(x-y)-2f(x)-2f(y))| --(0.2) where rho isfixed complex number with |๐บ|
์ฐธ๊ณ ๋ฌธํ (12)
- T. Aoki, "On the stability of the linear transformation in Banach spaces", J. Math. Soc. Japan, 2, pp.64~66 (1950)
- A. Chahbi, "On the generalized stability of d'Alembert functional equa-tion", J. Nonlinear Sci. Appl, 6, pp.198~204 (2013)
- P.W. Cholewa, "Remarks on the stability of functional equations", Aequationes Math, 27, pp.76~86 (1984)
- G.Z. Eskandani, "Hyers-Ulam-Rassias stability of pexiderized Cauchy functional equation in 2-Banach spaces", J. Nonlinear Sci. Appl, 5, pp.459~465 (2012)
- P. Gยทavruta, "A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings", J. Math. Anal. Appl, 184, pp.431~436 (1994)
- D.H. Hyers, "On the stability of the linear functional equation", Proc. Natl. Acad. Sci. U.S.A, 27, pp.222~224 (1941)
- C. Park, "Orthogonal stability of a cubic-quartic functional equation", J. Nonlinear Sci. Appl, 5, pp.28~36 (2012)
- M. Rassias, "On the stability of the linear mapping in Banach spaces", Proc. Amer. Math. Soc, 72, pp.297~300 (1978)
- K. Ravi, "Solution and stability of a reciprocal type functional equation in several variables", J. Nonlinear Sci. Appl, 7, pp.18~27 (2014)
- F. Skof, "Propriet locali e approssimazione di operatori", Rend. Sem. Mat. Fis. Milano, 53, pp.113~129 (1983)
- S.M. Ulam, "A Collection of the Mathematical Problems" (1960), Interscience Publ
- C. Zaharia, "On the probabilistic stability of the monomial functional equation", J. Non-linear Sci. Appl, 6, pp.51~59 (2013)
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