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《Journal of Xiamen University(Natural Science)》 2014-03
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Improved Theorem on Existence and Uniqueness of Fixed-point

SHI Ming-hui;JIANG Min;CHAO Fei;ZHOU Chang-le;Fujian Provincial Key Laboratory of Brain-like Intelligent Systems,School of Information Science and Engineering,Xiamen University;  
The problem of solving a nonlinear equation is generally transformed into the problem to search a fixed point of an iterative function.Furthermore,the latter is usually solved by an iterative method.The theorem to determine the existence and uniqueness of a fixed point in an iterative function is crucial to the iterative method,and is in general based on the Banach theorem of fixed point,in which two conditions regarding the iterative function should be examined.One condition is inner mapping condition(IMC),whereas the other is contraction mapping condition(CMC).In this paper,it is pointed out that IMC is so strict that it can be substituted by another relaxed condition,which is named by boundary condition(BC).Based on such an idea,an improved theorem is proposed,in which IMC is substituted by BC.Consequently,it is boundary values of the iterative function,rather than all values in the whole range involved that should be considered.Consequently,the analysis shows that,in application,the new theorem is more convenient and enjoys a wider range than the existing one.
【Fund】: 福建省自然科学基金(2010J01346)
【CateGory Index】: O241.7
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1 LING Yun;LI Man-zhi;College of Mathematics and Statistics,Hainan Normal University;Hainan Center for Mathematical Research;;The Properties of the General Solutions of the Special Riccati Equation[J];海南热带海洋学院学报;2017-02
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