Using a Razumikhin-type theorem,we obtain sufficient conditions for the global asymptotic stability of the zero solution of a certain fourth order functional differential equations.The result generalizes the well know...Using a Razumikhin-type theorem,we obtain sufficient conditions for the global asymptotic stability of the zero solution of a certain fourth order functional differential equations.The result generalizes the well known results.展开更多
Given two positive constants α and β, we prove that the integral inequality ∫_0^1f^α＋β（x）dx≥∫_0^1∫^α（x）x^β dx holds for all non-negative valued continuous functions ∫ satisfying ∫_x^1f（t）dt≥∫_x^1t...Given two positive constants α and β, we prove that the integral inequality ∫_0^1f^α＋β（x）dx≥∫_0^1∫^α（x）x^β dx holds for all non-negative valued continuous functions ∫ satisfying ∫_x^1f（t）dt≥∫_x^1tdt for x∈[0,1] if and only if α＋β≥1.This solves an open problem proposed recently by Ngo, Thang, Dat, and Tuan.展开更多
A Bernstein type theorem and a converse theorem of best approximation by polynomials in Bergman spaces Hq^p(p>0,q>1) are proved.Some proofs and results in [1] are in proved.
基金The project is supported by Natural Science Foundation of Hebei Provice.
文摘Using a Razumikhin-type theorem,we obtain sufficient conditions for the global asymptotic stability of the zero solution of a certain fourth order functional differential equations.The result generalizes the well known results.
文摘Given two positive constants α and β, we prove that the integral inequality ∫_0^1f^α＋β（x）dx≥∫_0^1∫^α（x）x^β dx holds for all non-negative valued continuous functions ∫ satisfying ∫_x^1f（t）dt≥∫_x^1tdt for x∈[0,1] if and only if α＋β≥1.This solves an open problem proposed recently by Ngo, Thang, Dat, and Tuan.
基金This paper is a part of the author's series of letures at the Mathematical Institute of the Hungarian Academy of Sciences while visiting Hungary sent by the state Education Committee,the People's Republic of China.
文摘A Bernstein type theorem and a converse theorem of best approximation by polynomials in Bergman spaces Hq^p(p>0,q>1) are proved.Some proofs and results in [1] are in proved.
