本文利用优化理论及拟范数的性质研究了与Hayajneh-Kittaneh猜想相关的算子不等式.设E(M)是非交换对称拟Banach空间,x_(i)∈E(M)^((p)+),y_(i)∈E(M)^((q)+)使得x_(i)y_(i)=y_(i)x_(i),i=1,2,…,n,我们证明了||(∑^(k)_(j)=1 x^(1/2)^(i...本文利用优化理论及拟范数的性质研究了与Hayajneh-Kittaneh猜想相关的算子不等式.设E(M)是非交换对称拟Banach空间,x_(i)∈E(M)^((p)+),y_(i)∈E(M)^((q)+)使得x_(i)y_(i)=y_(i)x_(i),i=1,2,…,n,我们证明了||(∑^(k)_(j)=1 x^(1/2)^(i)y^(1/2)_(i))^(2)||E(M)^((r))≤(∑^(k)_(j)=1_(xi))^(1/2)(∑^(k)_(j)=1 y i)(∑^(k)_(j)=1 x i)^(1/2)||E(M)^((r))≤||(∑^(k)_(j)=1 x i)(∑^(k)_(j)=1 y i)||E(M)^((r)).其中1≤p,q,r<∞且1/r=1/p+1/q.同时我们还给出了一些与log-次优化相关的不等式.展开更多
In this paper,we discuss the calculations of fixed point indexs for multivalued condensing mappings and k-set-contraction mappings,obtain some theorems on the eigenvalues and the fixed points under the suitable condit...In this paper,we discuss the calculations of fixed point indexs for multivalued condensing mappings and k-set-contraction mappings,obtain some theorems on the eigenvalues and the fixed points under the suitable conditions. Our conclusions improve and generalize some well-known results.展开更多
In this paper, a new existence theorem of anti-periodic solutions for a class ofstrongly nonlinear evolution equations in Banach spaces is presented. The equations contain nonlinear monotone operators and a nonmonoton...In this paper, a new existence theorem of anti-periodic solutions for a class ofstrongly nonlinear evolution equations in Banach spaces is presented. The equations contain nonlinear monotone operators and a nonmonotone perturbation. Moreover, throughan appropriate transformation, the existence of anti-periodic solutions for a class of secondorder nonlinear evolution equations is verified. Our abstract results are illustrated by anexample from quasi-linear partial differential equations with time anti-periodic conditionsand an example from quasi-linear anti-periodic hyperbolic differential equations.展开更多
文摘本文利用优化理论及拟范数的性质研究了与Hayajneh-Kittaneh猜想相关的算子不等式.设E(M)是非交换对称拟Banach空间,x_(i)∈E(M)^((p)+),y_(i)∈E(M)^((q)+)使得x_(i)y_(i)=y_(i)x_(i),i=1,2,…,n,我们证明了||(∑^(k)_(j)=1 x^(1/2)^(i)y^(1/2)_(i))^(2)||E(M)^((r))≤(∑^(k)_(j)=1_(xi))^(1/2)(∑^(k)_(j)=1 y i)(∑^(k)_(j)=1 x i)^(1/2)||E(M)^((r))≤||(∑^(k)_(j)=1 x i)(∑^(k)_(j)=1 y i)||E(M)^((r)).其中1≤p,q,r<∞且1/r=1/p+1/q.同时我们还给出了一些与log-次优化相关的不等式.
基金National Natural Science Foundation of the People’s Republic of China“Research on derivatives and operators in noncommutative symmetric spaces”(12261084).
文摘In this paper,we discuss the calculations of fixed point indexs for multivalued condensing mappings and k-set-contraction mappings,obtain some theorems on the eigenvalues and the fixed points under the suitable conditions. Our conclusions improve and generalize some well-known results.
基金The National science Foundation of the USA(Grant No．DMS 0400387)The University of Missouri Research Council(Grant No．URC-07-067)+1 种基金国家杰出青年基金(批准号：10425106)教育部“新世纪优秀人才”支持计划(批准号：04-0142)资助项目
基金This research is supported by the Science and Technology Committee of Guizhou Province,China(20023002)
文摘In this paper, a new existence theorem of anti-periodic solutions for a class ofstrongly nonlinear evolution equations in Banach spaces is presented. The equations contain nonlinear monotone operators and a nonmonotone perturbation. Moreover, throughan appropriate transformation, the existence of anti-periodic solutions for a class of secondorder nonlinear evolution equations is verified. Our abstract results are illustrated by anexample from quasi-linear partial differential equations with time anti-periodic conditionsand an example from quasi-linear anti-periodic hyperbolic differential equations.
