β—半可微k—集压缩映射的正不动点定理及其在传染病模型中的应用  

POSITIVE FIXED POINT THEOREMS FOR β-SEMIDIFFERENTIABLE κ -SET-CONTRACTIVE MAPPINGS WITH APPLICATION TO AN INFECTIOUS DISEASE MODEL

作　　者：刘威九 

机构地区：[1]Changsha Normal University of Water Resources and Electric Power, Changsha 410077

出　　处：《高校应用数学学报（A辑）》1992年第1期 91-101,共11页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：Supported by the University Natural Science Foundation

摘　　要：In this paper we define the new concept of β -semidifferentiability of a mapping and obtain the positive fixed point theorems for β -semidifferentiable k -set-contractive mappings. Then the theorems are ap-plied to the nonlinear integral equation, x(t) = (s,x(s))ds , which can be interpreted as a modelfor the spread of certain infectious diseases, and the existence theorems of the positive solutions and positive eigenvalues for the equation are obtained.In this paper we define the new concept of β -semidifferentiability of a mapping and obtain the positive fixed point theorems for β -semidifferentiable k -set-contractive mappings. Then the theorems are ap-plied to the nonlinear integral equation, x(t) = (s,x(s))ds , which can be interpreted as a modelfor the spread of certain infectious diseases, and the existence theorems of the positive solutions and positive eigenvalues for the equation are obtained.

关 键 词：压缩映射 正不动点定理 传染病模型 

分 类 号：O189.2[理学—数学;理学—基础数学]