对偶锥映像上的问题
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摘要
本文研究了对偶锥映像上的一些非线性问题.利用拓扑度理论和半序的方法,获得了对偶锥映像的锐角原理,Debrunner-Flor不等式和不动点定理的结果.推广了一般单调映像的锐角原理和Debrunner-Flor不等式的一些结果.
In this paper, we study some nonlinear problems of dual cone mapping. By using topological degree theory and partial order methods, we get the results of the acute angle principle, Debrunner-Flor inequality and fixed point theorem for dual cone mapping. Some results in the document are improved and extended.
In this paper, we study some nonlinear problems of dual cone mapping. By using topological degree theory and partial order methods, we get the results of the acute angle principle, Debrunner-Flor inequality and fixed point theorem for dual cone mapping. Some results in the document are improved and extended.
引文
[1]郭大均.非线性泛函分析(第3版)[M].北京:高等教育出版社,2015.
[2]Deimling K.Nonlinear functional analysis[M].Berlin:Springer Press,1985.
[3]Bauer F L.An elementary proof of the Hopf inequality for positive operators[J].Numer.Math.,1965,17:331-337.
[4]Conway J B.A course in functional analysis(2nd ed.)[M].New York:Springer Press,1990.
[5]Chen Y Q,Cho Y J.Monotone type operators in nonreflexive Banach space[J].Fixed Point Theory Appl.,2014,2014:119.
[6]梁展东.Hilbert投影距离与范数的关系[J].系统科学与数学,1988,8(1):88-91.
[7]Browder F E.Degree of mapping for nonlinear mappings of monotone type[J].Proc.Nat.Acad.Sci.USA,1983,80:1771-1773.
[8]魏利,刘元星.Banach空间中m-d增生映射零点的强弱收敛定理[J].数学杂志,2016,36(3):573-583.
[9]崔玉军,邹玉梅.非线性算子的歧点[J].数学杂志,2011,31(3):476-480.
[2]Deimling K.Nonlinear functional analysis[M].Berlin:Springer Press,1985.
[3]Bauer F L.An elementary proof of the Hopf inequality for positive operators[J].Numer.Math.,1965,17:331-337.
[4]Conway J B.A course in functional analysis(2nd ed.)[M].New York:Springer Press,1990.
[5]Chen Y Q,Cho Y J.Monotone type operators in nonreflexive Banach space[J].Fixed Point Theory Appl.,2014,2014:119.
[6]梁展东.Hilbert投影距离与范数的关系[J].系统科学与数学,1988,8(1):88-91.
[7]Browder F E.Degree of mapping for nonlinear mappings of monotone type[J].Proc.Nat.Acad.Sci.USA,1983,80:1771-1773.
[8]魏利,刘元星.Banach空间中m-d增生映射零点的强弱收敛定理[J].数学杂志,2016,36(3):573-583.
[9]崔玉军,邹玉梅.非线性算子的歧点[J].数学杂志,2011,31(3):476-480.