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On the diamond-alpha Riemann integral and mean value theorems on time scales. (English) Zbl 1183.26041

Summary: We study diamond-alpha integrals on time scales. A diamond-alpha version of Fermat’s theorem for stationary points is also proved, as well as Rolle’s Lagrange’s, and Cauchy’s mean value theorems on time scales.

MSC:

26E70 Real analysis on time scales or measure chains
26A42 Integrals of Riemann, Stieltjes and Lebesgue type
39A12 Discrete version of topics in analysis
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