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

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.

Keywords

• Riemann generalized derivative
• (sigma,tau) differentiable functions
• monotonicity
• convexity
• symmetric derivative
• Schwarz derivative
• Darboux property