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