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Subdifferentials of convex functions on time scales

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  • The paper studies the notion of subdifferentials of functions defined on a time scale. The subdifferential of a given function $f$ is defined as the set of certain extended functions. Since the convexity of the given function guarantees its subdifferentiability, properties of convex functions on time scales are presented. We show that the convexity of a function is the necessary and sufficient condition for its subdifferentiability. The relations between the delta, nabla, diamond-$\alpha$ derivatives and subdifferentials of convex functions are given.
    Mathematics Subject Classification: Primary: 26D15, 39A13; Secondary: 52A40.


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