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| POSITIVE FIXED POINT THEOREMS FOR β-SEMIDIFFERENTIABLE κ -SET-CONTRACTIVE MAPPINGS WITH APPLICATION TO AN INFECTIOUS DISEASE MODEL | |
| 作者姓名： | 刘威九 |
| 作者单位： | Changsha Normal |
| 基金项目： | 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. |
| 关 键 词： | β-Semidifferentiable κ -Set-Contractive Map Positive Fixed Point Theorem Cone Infectious Disease Model Nonlinear Integral Equation Positive Periodic Solution. |
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