Order Preserving and Order Reversing Operators on the Class of L⁰-Convex Functions in Complete Random Normed Modules

Abstract

Based on both the fundamental theorem of affine geometry in regular L⁰-modules and the recent progress in random convex analysis, this paper characterizes the stable and fully order preserving and order reversing operators acting on the class of proper lower semicontinuous L⁰-convex functions in complete random normed modules.

Keywords

Order preserving operators / Order reversing operators / Fenchel conjugation / L⁰-convex functions / Complete random normed modules / Stability / 46N10 / 46B10 / 46H25

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