A surjection theorem and a fixed point theorem for a class of positive operators

被引:1
作者
Zhai Chengbo [1 ]
Guo Chunmei [1 ]
机构
[1] Shanxi Univ, Sch Math Sci, Inst Math, Taiyuan 030006, Shanxi, Peoples R China
基金
中国国家自然科学基金;
关键词
alpha-convex operator; normal and solid cone; surjection theorem; fixed point;
D O I
10.1016/j.jmaa.2007.04.032
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
This paper is concerned with alpha-convex operators on ordered Banach spaces. A surjection theorem for 1-convex operators in order intervals is established by means of the properties of cone and monotone iterative technique. It is assumed that 1-convex operator A is increasing and satisfies Ay - Ax <= M(y - x) for theta <= x <= y <= nu(0), where theta denotes the zero element and nu(0) is a constant. Moreover, we prove a fixed point theorem for alpha (> 1)-convex operators by using fixed point theorem of cone expansion. In the end, we apply the fixed point theorem to certain integral equations. (c) 2007 Elsevier Inc. All rights reserved.
引用
收藏
页码:976 / 983
页数:8
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