In this article, the authors establish some new nonlinear difference inequalities in two independent variables, which generalize some existing results and can be used as handy tools in the study of qualitative as well...In this article, the authors establish some new nonlinear difference inequalities in two independent variables, which generalize some existing results and can be used as handy tools in the study of qualitative as well as quantitative properties of solutions of certain classes of difference equations.展开更多
Let Ak be an integral operator defined by Akf（x）：=1K（x）∫Ω2k（x,y）f（y）dμ2（y）where k：Ω1× Ω2 →Ris a general nonnegative kernel, （Ω1,∑1,μ1）, （Ω2,∑2,μ2） are measure spaces with a-finite meas...Let Ak be an integral operator defined by Akf（x）：=1K（x）∫Ω2k（x,y）f（y）dμ2（y）where k：Ω1× Ω2 →Ris a general nonnegative kernel, （Ω1,∑1,μ1）, （Ω2,∑2,μ2） are measure spaces with a-finite measures and K（x）：=∫Ω2k（x,y）dμ2（y）,x∈Ω1.In this paper improvements and reverses of new weighted Hardy type inequalities with integral operators of such type are stated and proved. New Cauchy type mean is introduced and monotonicity property of this mean is proved.展开更多
基金a HKU Seed grant the Research Grants Council of the Hong Kong SAR(HKU7016/07P)
文摘In this article, the authors establish some new nonlinear difference inequalities in two independent variables, which generalize some existing results and can be used as handy tools in the study of qualitative as well as quantitative properties of solutions of certain classes of difference equations.
文摘Let Ak be an integral operator defined by Akf（x）：=1K（x）∫Ω2k（x,y）f（y）dμ2（y）where k：Ω1× Ω2 →Ris a general nonnegative kernel, （Ω1,∑1,μ1）, （Ω2,∑2,μ2） are measure spaces with a-finite measures and K（x）：=∫Ω2k（x,y）dμ2（y）,x∈Ω1.In this paper improvements and reverses of new weighted Hardy type inequalities with integral operators of such type are stated and proved. New Cauchy type mean is introduced and monotonicity property of this mean is proved.
