Based on the topological degree for 1-set-contractive fields established in [11], we discuss the 1-set-contractive perturbation and the existence of zero points for nonlinear equations with accretive mappings in Menge...Based on the topological degree for 1-set-contractive fields established in [11], we discuss the 1-set-contractive perturbation and the existence of zero points for nonlinear equations with accretive mappings in Menger PN-spaces and obtain some new results.展开更多
In this paper, we will prove that Ky Fan’s Theorem (Math. Z. 112(1969), 234-240) is true for 1-set-contractive maps defined on a bounded closed convex subset K in a Banach space with int K≠ . This class of 1-set-con...In this paper, we will prove that Ky Fan’s Theorem (Math. Z. 112(1969), 234-240) is true for 1-set-contractive maps defined on a bounded closed convex subset K in a Banach space with int K≠ . This class of 1-set-contractive maps includes condensing maps, nonexpansive maps, semicontractive maps, LANE maps and others. As applications of our theorems, some fixed point theorems of non-self- maps are proved under various well-known boundary conditions. Our results are generalizations and improvements of the recent results obtained by many authors.展开更多
利用Petryshyn W V(1972)中所定义的1-集压缩映象拓扑度的一些基本性质以及半闭1-集压缩映象的诸多性质讨论Banach空间中一类算子的固有值与固有元的存在性问题。当算子满足一些较弱的条件时,可以保证至少存在一个大于1的固有值以及在...利用Petryshyn W V(1972)中所定义的1-集压缩映象拓扑度的一些基本性质以及半闭1-集压缩映象的诸多性质讨论Banach空间中一类算子的固有值与固有元的存在性问题。当算子满足一些较弱的条件时,可以保证至少存在一个大于1的固有值以及在其定义域的边界上存在对应的固有元。这些结论可以用来帮助探讨非线性算子方程或方程组的解的存在性问题以及解的具体形式问题。展开更多
基金Supported by the National Natural Science Foundation of China(11071108)the Natural Science Foundation of Jiangxi Province of China(2010GZS0147)
文摘Based on the topological degree for 1-set-contractive fields established in [11], we discuss the 1-set-contractive perturbation and the existence of zero points for nonlinear equations with accretive mappings in Menger PN-spaces and obtain some new results.
基金Project supported by the National Natural Science Foundation of ChinaNatural Science Foundation of Shandong Province of China
文摘In this paper, we will prove that Ky Fan’s Theorem (Math. Z. 112(1969), 234-240) is true for 1-set-contractive maps defined on a bounded closed convex subset K in a Banach space with int K≠ . This class of 1-set-contractive maps includes condensing maps, nonexpansive maps, semicontractive maps, LANE maps and others. As applications of our theorems, some fixed point theorems of non-self- maps are proved under various well-known boundary conditions. Our results are generalizations and improvements of the recent results obtained by many authors.
文摘利用Petryshyn W V(1972)中所定义的1-集压缩映象拓扑度的一些基本性质以及半闭1-集压缩映象的诸多性质讨论Banach空间中一类算子的固有值与固有元的存在性问题。当算子满足一些较弱的条件时,可以保证至少存在一个大于1的固有值以及在其定义域的边界上存在对应的固有元。这些结论可以用来帮助探讨非线性算子方程或方程组的解的存在性问题以及解的具体形式问题。
