Sufficient conditions are given to assert that two differentiable mappings between Banach spaces have common values. The proof is essentially based upon continuation methods.
E E. Browder and W. V. Petryshyn defined the topological degree for A- proper mappings and then W. V. Petryshyn studied a class of A-proper mappings, namely, P1-compact mappings and obtained a number of important fixe...E E. Browder and W. V. Petryshyn defined the topological degree for A- proper mappings and then W. V. Petryshyn studied a class of A-proper mappings, namely, P1-compact mappings and obtained a number of important fixed point theorems by virtue of the topological degree theory. In this paper, following W. V. Petryshyn, we continue to study P1-compact mappings and investigate the boundary condition, under which many new fixed point theorems of P1-compact mappings are obtained. On the other hand, this class of A-proper mappings with the boundedness property includes completely continuous operators and so, certain interesting new fixed point theorems for completely continuous operators are obtained immediately. As a result of it, our results generalize several famous theorems such as Leray-Schauder＇s theorem, Rothe＇s theorem, Altman＇s theorem, Petryshyn＇s theorem, etc.展开更多
Building compact 3D maps of the environment models has become an important research topic. This paper presented an efficient stream decimation algorithm of massive meshes. The algorithm adapted the pre-processing step...Building compact 3D maps of the environment models has become an important research topic. This paper presented an efficient stream decimation algorithm of massive meshes. The algorithm adapted the pre-processing step leading to lower in-corn memory consumption. This algorithm is applied to reconstructing compact terrain with mobile robot, achieving satisfying results.展开更多
This paper gives internal characterizations of some sequence covering compact images and compact covering compact images of paracompact locally compact spaces, which improve some results on compact images of locally...This paper gives internal characterizations of some sequence covering compact images and compact covering compact images of paracompact locally compact spaces, which improve some results on compact images of locally compact metric spaces.展开更多
Sufficient conditions were given to assert that between any two Banach spaces over K, Fredholm mappings share at least one .value in a specific open ball. The proof of the result is constructive and based upon continu...Sufficient conditions were given to assert that between any two Banach spaces over K, Fredholm mappings share at least one .value in a specific open ball. The proof of the result is constructive and based upon continuation methods.展开更多
The main purpose of the present work is to introduce necessary conditions for a map on a non-metric space, defined by using a map on a metric space, to have a fixed point.
Our purpose is to introduce new necessary conditions for a fixed point of maps on non-metric spaces. We use a contraction map on a metric topological space and a lately published definition of limit of a function betw...Our purpose is to introduce new necessary conditions for a fixed point of maps on non-metric spaces. We use a contraction map on a metric topological space and a lately published definition of limit of a function between the metric topological space and the non-metric topological space. Then we show that we can create a function h on the non-metric space Y, h :Y →Y and present necessary conditions for a fixed point of this map on this map on Y. Therefore, this gives an opportunity to take a best conclusion in some sense, when non-metrizable matter is under consideration.展开更多
文摘Sufficient conditions are given to assert that two differentiable mappings between Banach spaces have common values. The proof is essentially based upon continuation methods.
基金Supported in part by Education Ministry,Anhui Province,China(No:2003kj047zd)
文摘E E. Browder and W. V. Petryshyn defined the topological degree for A- proper mappings and then W. V. Petryshyn studied a class of A-proper mappings, namely, P1-compact mappings and obtained a number of important fixed point theorems by virtue of the topological degree theory. In this paper, following W. V. Petryshyn, we continue to study P1-compact mappings and investigate the boundary condition, under which many new fixed point theorems of P1-compact mappings are obtained. On the other hand, this class of A-proper mappings with the boundedness property includes completely continuous operators and so, certain interesting new fixed point theorems for completely continuous operators are obtained immediately. As a result of it, our results generalize several famous theorems such as Leray-Schauder＇s theorem, Rothe＇s theorem, Altman＇s theorem, Petryshyn＇s theorem, etc.
文摘Building compact 3D maps of the environment models has become an important research topic. This paper presented an efficient stream decimation algorithm of massive meshes. The algorithm adapted the pre-processing step leading to lower in-corn memory consumption. This algorithm is applied to reconstructing compact terrain with mobile robot, achieving satisfying results.
文摘This paper gives internal characterizations of some sequence covering compact images and compact covering compact images of paracompact locally compact spaces, which improve some results on compact images of locally compact metric spaces.
基金Project supported by D.G.E.S. Pb 96-1338-CO 2-01 and the Junta de Andalucia
文摘Sufficient conditions were given to assert that between any two Banach spaces over K, Fredholm mappings share at least one .value in a specific open ball. The proof of the result is constructive and based upon continuation methods.
文摘The main purpose of the present work is to introduce necessary conditions for a map on a non-metric space, defined by using a map on a metric space, to have a fixed point.
文摘Our purpose is to introduce new necessary conditions for a fixed point of maps on non-metric spaces. We use a contraction map on a metric topological space and a lately published definition of limit of a function between the metric topological space and the non-metric topological space. Then we show that we can create a function h on the non-metric space Y, h :Y →Y and present necessary conditions for a fixed point of this map on this map on Y. Therefore, this gives an opportunity to take a best conclusion in some sense, when non-metrizable matter is under consideration.
