In this paper we develop the Banach contraction principle and Kannan fixed point theorem on generalized cone metric spaces. We prove a version of Suzuki and Kannan type generalizations of fixed point theorems in gener...In this paper we develop the Banach contraction principle and Kannan fixed point theorem on generalized cone metric spaces. We prove a version of Suzuki and Kannan type generalizations of fixed point theorems in generalized cone metric spaces.展开更多
Boltzmann equation is an equation which is related to the three variables of x, v, t. In this paper, we mainly study the space-uniform Boltzmann equation which unknown function F is not related to the position variabl...Boltzmann equation is an equation which is related to the three variables of x, v, t. In this paper, we mainly study the space-uniform Boltzmann equation which unknown function F is not related to the position variable x. We mainly use the contraction mapping theorem to find the existence of the solution, so our mainly work is to prove the self-mapping, i.e. to prove its uniformly bounded, and then to prove the contraction mapping. There we can get the range of ||B(θ)||L1(L∞), next we can figure out the range of M and T from the conditions what we know. Finally, from these conditions, we can find the existence of the solution.展开更多
In this paper, we introduce a G metric on the G-cone metric space and then prove that a complete G-cone metric space is always a complete G metric space and verify that a contractive mapping on the G-cone metric space...In this paper, we introduce a G metric on the G-cone metric space and then prove that a complete G-cone metric space is always a complete G metric space and verify that a contractive mapping on the G-cone metric space is a contractive mapping on the G metric space. At last, we also give a new way to obtain the unique fixed point on G-cone metric space.展开更多
本文主要结果:设向量泛函(x)和(x)分别是 F 上实连续凹凸泛函,(tx)对每个 x∈F 关于 t 在[0,+∞)上严格单调且(θ)<,(θ)≥.又设=(a_1,a_2,…,a_n)>,(θ)<=(d_1,d_2,…d_n)<.设集值映射是凝聚的且下列条件满足:(1)若.则(2)...本文主要结果:设向量泛函(x)和(x)分别是 F 上实连续凹凸泛函,(tx)对每个 x∈F 关于 t 在[0,+∞)上严格单调且(θ)<,(θ)≥.又设=(a_1,a_2,…,a_n)>,(θ)<=(d_1,d_2,…d_n)<.设集值映射是凝聚的且下列条件满足:(1)若.则(2)令.存在 i_0,j_0使得 d_i_0≤r_i_0j_0;(3)若对某个β_j(x)=d_j,λ≥1,有λxTx;(4){x∈F|存在1≤j≤m 使得:(5)若,对某个β_j(x)=0,λ≥1,有λxTx.那么 T 三个不动点.展开更多
文摘In this paper we develop the Banach contraction principle and Kannan fixed point theorem on generalized cone metric spaces. We prove a version of Suzuki and Kannan type generalizations of fixed point theorems in generalized cone metric spaces.
文摘Boltzmann equation is an equation which is related to the three variables of x, v, t. In this paper, we mainly study the space-uniform Boltzmann equation which unknown function F is not related to the position variable x. We mainly use the contraction mapping theorem to find the existence of the solution, so our mainly work is to prove the self-mapping, i.e. to prove its uniformly bounded, and then to prove the contraction mapping. There we can get the range of ||B(θ)||L1(L∞), next we can figure out the range of M and T from the conditions what we know. Finally, from these conditions, we can find the existence of the solution.
基金Supported by the Natural Science Foundation of Hubei Province Education Department （Q20132505） Supported by the PhD Start-up Fund of Hanshan Normal University of Guangdong Province（QD20110920）
文摘In this paper, we introduce a G metric on the G-cone metric space and then prove that a complete G-cone metric space is always a complete G metric space and verify that a contractive mapping on the G-cone metric space is a contractive mapping on the G metric space. At last, we also give a new way to obtain the unique fixed point on G-cone metric space.
文摘本文主要结果:设向量泛函(x)和(x)分别是 F 上实连续凹凸泛函,(tx)对每个 x∈F 关于 t 在[0,+∞)上严格单调且(θ)<,(θ)≥.又设=(a_1,a_2,…,a_n)>,(θ)<=(d_1,d_2,…d_n)<.设集值映射是凝聚的且下列条件满足:(1)若.则(2)令.存在 i_0,j_0使得 d_i_0≤r_i_0j_0;(3)若对某个β_j(x)=d_j,λ≥1,有λxTx;(4){x∈F|存在1≤j≤m 使得:(5)若,对某个β_j(x)=0,λ≥1,有λxTx.那么 T 三个不动点.
