Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 187, pp. 1-14.
Title: The role of Riemann generalized derivative in the
study of qualitative properties of functions
Authors: Sorin Radulescu (Institute of Math. Statistics, Bucharest, Romania)
Petrus Alexandrescu (Institute of Math. Statistics, Bucharest, Romania)
Diana-Olimpia Alexandrescu (Univ. of Craiova,Craiova, Romania)
Abstract:
Marshal Ash [3] introduced the concept of (sigma,tau)
differentiable functions and studied the Riemann generalized derivatives
In this article we study the convexity and monotonicity of (sigma,tau)
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 (sigma,tau) differentiable functions.
Submitted April 23, 2013. Published August 23, 2013.
Math Subject Classifications: 26A24, 28A15
Key Words: Riemann generalized derivative; (sigma,tau) differentiable functions;
monotonicity; convexity; symmetric derivative; Schwarz derivative;
Darboux property.