Estimates to the stability of functional equations
Given a function f mapping a groupoid (X, $${\diamond} $$) into a metric groupoid (Y,*, d)
and satisfying the inequality $$ d (f (x\diamond y), f (x)* f (y))\leq\varepsilon (x, y)\quad (x,
y\in X), $$ the problem of stability in the sense of Hyers-Ulam is to construct a solution g of
the functional equation $$ g (x\diamond y)= g (x)* g (y)\quad (x, y\in X) $$ and to obtain
estimates for the pointwise distance between g and f. Applying the so-called direct method,
the stability problem for more general functional equations is also investigated.
and satisfying the inequality $$ d (f (x\diamond y), f (x)* f (y))\leq\varepsilon (x, y)\quad (x,
y\in X), $$ the problem of stability in the sense of Hyers-Ulam is to construct a solution g of
the functional equation $$ g (x\diamond y)= g (x)* g (y)\quad (x, y\in X) $$ and to obtain
estimates for the pointwise distance between g and f. Applying the so-called direct method,
the stability problem for more general functional equations is also investigated.
Summary
Given a function f mapping a groupoid (X,
) into a metric groupoid (Y, * ,d) and satisfying the inequality $$ d(f(x \diamond y),f(x)*f(y))\leq \varepsilon(x,y)\quad (x,y \in X), $$ the problem of stability in the sense of Hyers-Ulam is to construct a solution g of the functional equation
and to obtain estimates for the pointwise distance between g and f. Applying the so-called direct method, the stability problem for more general functional equations is also investigated.
infona.pl
以上显示的是最相近的搜索结果。 查看全部搜索结果