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Mean value theorems in \(q\)-calculus. (English) Zbl 1058.39018

The main results include \(q\)-analogues for the Rolle and Lagrange theorem concerning Euler-Jackson \(q\)-derivative, the mean-value theorems for \(q\)-integrals and estimation of remainder term in \(q\)-Taylor formula. Some applications on \(q\)-iterative methods are given.

MSC:

39A13 Difference equations, scaling (\(q\)-differences)
33D05 \(q\)-gamma functions, \(q\)-beta functions and integrals
05A30 \(q\)-calculus and related topics
26A24 Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems
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