On α-convex operators

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Abstract

In this paper, the existence and uniqueness of positive fixed points for a class of convex operators is obtained by means of the properties of cone, concave operators and the monotonicity of set-valued maps. In the end, we give a simple application to certain integral equations.

Keywords

α-Convex operator
Normal cone
Positive fixed point

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This work was supported by Fund of National Natural Science of China (10371068).