In this article, we prove that the symmetric function Fn（x,r）=∑i1＋i2＋……in=r（x1（i1x2^i2……xn^in）1/r is Schur harmonic convex for x ∈ R＋n and r ∈N -=（1, 2, 3,...} As its applications, some analytic inequa...In this article, we prove that the symmetric function Fn（x,r）=∑i1＋i2＋……in=r（x1（i1x2^i2……xn^in）1/r is Schur harmonic convex for x ∈ R＋n and r ∈N -=（1, 2, 3,...} As its applications, some analytic inequalities are established.展开更多
In this paper we discuss a relatively general kind of iterative functional equation G(x,f(x), ...,f n (x)) = 0 (for allx ∈J), whereJ is a connected closed subset of the real number axis ?,G∈C m (J n+1, ?) andn ≥ 2....In this paper we discuss a relatively general kind of iterative functional equation G(x,f(x), ...,f n (x)) = 0 (for allx ∈J), whereJ is a connected closed subset of the real number axis ?,G∈C m (J n+1, ?) andn ≥ 2. Using the method of approximating fixed points by small shift of maps, choosing suitable metrics on functional spaces and finding a relation between uniqueness and stability of fixed points of maps of general spaces, we prove the existence, uniqueness and stability ofCm solutions of the above equation for any integer m ≥ 0 under relatively weak conditions, and generalize related results in reference in different aspects.展开更多
基金supported by NSFC (60850005)NSF of Zhejiang Province(D7080080, Y7080185, Y607128)
文摘In this article, we prove that the symmetric function Fn（x,r）=∑i1＋i2＋……in=r（x1（i1x2^i2……xn^in）1/r is Schur harmonic convex for x ∈ R＋n and r ∈N -=（1, 2, 3,...} As its applications, some analytic inequalities are established.
文摘In this paper we discuss a relatively general kind of iterative functional equation G(x,f(x), ...,f n (x)) = 0 (for allx ∈J), whereJ is a connected closed subset of the real number axis ?,G∈C m (J n+1, ?) andn ≥ 2. Using the method of approximating fixed points by small shift of maps, choosing suitable metrics on functional spaces and finding a relation between uniqueness and stability of fixed points of maps of general spaces, we prove the existence, uniqueness and stability ofCm solutions of the above equation for any integer m ≥ 0 under relatively weak conditions, and generalize related results in reference in different aspects.
