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In this paper, by using fixed point theorem, we obtain the stability of the following functional equations \begin{align*} f(pr,qs)+g(ps,qr)&=\theta(p,q, r,s)f(p,q)h(r,s) \\ f(pr,qs)+g(ps,qr)&=\theta(p,q, r,s)g(p,q)h(r,s), \end{align*} where $G$ is a commutative semigroup, $\theta : G^{4} \rightarrow \mathbb{R}_{k}$ a function and $f,g,h$ are functionals on $G^{2}$.
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참고문헌 (23)
참고문헌 신청
Janusz Brzdȩk / 2015 / Two general theorems on superstability of functional equations / Aequationes mathematicae 89(3):771~783
J. K. Chung / 1989 / Measures of distance between probability distributions / J. Math. Anal. Appl 138:280~292
J. B. Diaz / 1968 / A fixed point theorem of the alternative, for contrac-tions on a generalized complete metric space / Bulletin of the American Mathe-matical Society 74:305~309
M. Hosszu / 1971 / On the functional equation f(x+y,z)+f(x, y) = f(x, y+z)+f(y, z) / Periodica Math. Hungarica 1(3):213~216
Pl. Kannappan / 1997 / Sum form distance measures between probability distributions and functional equations / Int. J. of Math. & Stat. Sci 6:91~105
J. K. Chung / 1989 / Measures of distance between probability distributions / J. Math. Anal. Appl 138:280~292
J. B. Diaz / 1968 / A fixed point theorem of the alternative, for contrac-tions on a generalized complete metric space / Bulletin of the American Mathe-matical Society 74:305~309
M. Hosszu / 1971 / On the functional equation f(x+y,z)+f(x, y) = f(x, y+z)+f(y, z) / Periodica Math. Hungarica 1(3):213~216
Pl. Kannappan / 1997 / Sum form distance measures between probability distributions and functional equations / Int. J. of Math. & Stat. Sci 6:91~105
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