Electron. J. Diff. Equ., Vol. 2013 (2013), No. 187, pp. 1-14.

The role of Riemann generalized derivative in the study of qualitative properties of functions

Sorin Radulescu, Petrus Alexandrescu, Diana-Olimpia Alexandrescu

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.

Show me the PDF file (226 KB), TEX file, and other files for this article.

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

Return to the EJDE web page