A surjection theorem and a fixed point theorem for a class of positive operators |
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Authors: | Chengbo Zhai Chunmei Guo |
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Institution: | Institute of Mathematics, School of Mathematics Science, Shanxi University, Taiyuan 030006, Shanxi, People's Republic of China |
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Abstract: | This paper is concerned with α-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 θ?x?y?v0, where θ denotes the zero element and v0 is a constant. Moreover, we prove a fixed point theorem for -convex operators by using fixed point theorem of cone expansion. In the end, we apply the fixed point theorem to certain integral equations. |
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Keywords: | α-Convex operator Normal and solid cone Surjection theorem Fixed point |
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