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A mean value theorem for internal functions and an estimation for the differential mean point. (English) Zbl 1274.26081

Summary: We present several results about the mean value theorem (MVT) with techniques from nonstandard analysis. Using only the intermediate value theorem, we present a nonstandard proof of the MVT and we extend the MVT for internal SU-differentiable functions. In the end we discuss the location of the differential mean point \(c\) in the segment \([x,y]\), as \(y\to x\).

MSC:

26E35 Nonstandard analysis
26B05 Continuity and differentiation questions
46S20 Nonstandard functional analysis
46T20 Continuous and differentiable maps in nonlinear functional analysis
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