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

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.

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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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