一类抽象二元非线性算子的不动点的存在性与唯一性

Abstract

Abstract:

In this paper, we study the existence and uniqueness of fixed points for a class of abstract binary nonlinear operators, by means of the properties of cone, monotone iterative methods and spectral radius conditions of related positive bounded linear operators in partially ordered Banach spaces; and then generalize and improve a classical theorem, and so obtain several new results. Finally, we present an application to initial value problems of first order nonlinear ordinary differential equations.

Key words: Normal cone, Positive bounded linear operator, Spectral radius, Nonlinear operator, Fixed point

CLC Number:

O177.91

Ping Shi. Existence and Uniqueness of Fixed Points for a Class of Abstract Binary Nonlinear Operators[J].Acta mathematica scientia,Series A, 2020, 40(4): 882-890.

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References 9

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Existence and Uniqueness of Fixed Points for a Class of Abstract Binary Nonlinear Operators

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