For a positive integer s,the projection body of an s-concave function f:R^(n)→[0,+∞),a convex body in the(n+s)-dimensional Euclidean space R^(n+s),is introduced.Associated inequalities for s-concave functions,such a...For a positive integer s,the projection body of an s-concave function f:R^(n)→[0,+∞),a convex body in the(n+s)-dimensional Euclidean space R^(n+s),is introduced.Associated inequalities for s-concave functions,such as,the functional isoperimetric inequality,the functional Petty projection inequality and the functional Loomis-Whitney inequality are obtained.展开更多
In this paper, we prove the existence and uniqueness of positive periodic solutions for first-order functional differential equation y＇（t） = α（t）y（t） ＋ f（t, y（t -τ-（t））） ＋ g（t）by using two fixed poi...In this paper, we prove the existence and uniqueness of positive periodic solutions for first-order functional differential equation y＇（t） = α（t）y（t） ＋ f（t, y（t -τ-（t））） ＋ g（t）by using two fixed point theorems of general α-concave operators and homogeneous operators in ordered Banach spaces.展开更多
基金supported by the National Natural Science Foundation of China(Nos.12001291,12071318)Chern Institute of Mathematics,Nankai University。
文摘For a positive integer s,the projection body of an s-concave function f:R^(n)→[0,+∞),a convex body in the(n+s)-dimensional Euclidean space R^(n+s),is introduced.Associated inequalities for s-concave functions,such as,the functional isoperimetric inequality,the functional Petty projection inequality and the functional Loomis-Whitney inequality are obtained.
基金Supported by the Youth Science Foundation of China（l1201272） Supported by the Youth Science Foundatioa of Shanxi Province（2010021002-1）
文摘In this paper, we prove the existence and uniqueness of positive periodic solutions for first-order functional differential equation y＇（t） = α（t）y（t） ＋ f（t, y（t -τ-（t））） ＋ g（t）by using two fixed point theorems of general α-concave operators and homogeneous operators in ordered Banach spaces.
