Sorin Radulescu, Petrus Alexandrescu, Diana-Olimpia Alexandrescu
Abstract:
Marshal Ash [3] introduced the concept of
differentiable functions and studied the Riemann generalized derivatives
In this article we study the convexity and monotonicity of
differentiable functions, using results by Hincin, Humke and Laczkovich,
and using the Riemann generalized derivative.
We give conditions such that the classic properties of differentiable
functions hold also for
differentiable functions.
Submitted April 23, 2013. Published August 23, 2013.
Math Subject Classifications: 26A24, 28A15
Key Words: Riemann generalized derivative;
differentiable functions;
monotonicity; convexity; symmetric derivative; Schwarz derivative;
Darboux property.
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Sorin Radulescu Institute of Mathematical Statistics and Applied Mathematics Calea 13 Septembrie, no. 13, Bucharest 5, RO-050711, Romania email: xsradulescu@gmail.com | |
Petrus Alexandrescu Institute of sociology, Casa Academiei Romane Calea 13 Septembrie, no. 13, Bucharest 5, RO-050711, Romania email: alexandrescu_petrus@yahoo.com | |
Diana-Olimpia Alexandrescu Department of Mathematics, University of Craiova 200585 Craiova, Romania email: alexandrescudiana@yahoo.com |
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