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Generalizations of the Lagrange mean value theorem and applications

Mateljević Miodrag (University of Belgrade, Faculty of Mathematics, Belgrade)
Svetlik Marek (University of Belgrade, Faculty of Mathematics, Belgrade)
Albijanić Miloljub (Faculty of Economics, Finance and Administration, Belgrade)
Savić Nebojša (Faculty of Economics, Finance and Administration, Belgrade)

In this paper we give a generalization of the Lagrange mean value theorem via lower and upper derivative, as well as appropriate criteria of monotonicity and convexity for arbitrary function f : (a, b) ( R. Some applications to the neoclassical economic growth model are given (from mathematical point of view).

Keywords: Upper and lower derivative, generalization of the Lagrange mean value theorem, characterization of monotone and convex functions, the neoclassical economic growth model