References
- Proc. Amer. Math. Soc. v.80 The stability of the cosine equation J. Baker
- Proc. Amer. Math. Soc. v.74 The stability of the equation f(x + y) = f(x)f(y) J. Baker
Communications of the Korean Mathematical Society (대한수학회논문집)
- Volume 12 Issue 2
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- Pages.287-291
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- 1997
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- 1225-1763(pISSN)
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- 2234-3024(eISSN)
ON THE SUPERSTABILITY OF SOME FUNCTIONAL INEQUALITIES WITH THE UNBOUNDED CAUCHY DIFFERENCE (x+y)-f(x)f(y)
- Jung, Soon-Mo (Mathematics Section College of Science & Technology Hong-Ik University)
- Published : 1997.04.01
Abstract
Assume $H_i : R_+ \times R_+ \to R_+ (i = 1, 2)$ are monotonically increasing (in both variables), homogeneous mapping for which $H_1(tu, tv) = t^p(H_1(u, v) (p > 0)$ and $H_2(u, v)^{t^q} (q \leq 1)$ hold for $t, u, v \geq 0$. Using an idea from the paper of Baker, Lawrence and Zorzitto [2], the superstability problems of the functional inequalities $\Vert f(x+y) - f(x)f(y) \Vert \leq H_i (\Vert x \Vert, \Vert y \Vert)$ shall be investigated.