Rajković, Predrag M.; Stanković, Miomir S.; Marinković, Slađana D. Mean value theorems in \(q\)-calculus. (English) Zbl 1058.39018 Mat. Vesn. 54, No. 3-4, 171-178 (2002). 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. Reviewer: Ljubiša Kocić (Niš) Cited in 19 Documents 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 Keywords:Lagrange theorem; Euler-Jackson \(q\)-derivative; mean-value theorems; \(q\)-integrals; \(q\)-Taylor formula; \(q\)-iterative methods; Rolle’s theorem PDFBibTeX XMLCite \textit{P. M. Rajković} et al., Mat. Vesn. 54, No. 3--4, 171--178 (2002; Zbl 1058.39018) Full Text: EuDML