Sorin Radulescu, Petrus Alexandrescu, Diana-Olimpia Alexandrescu
Abstract:
Initiated by Marshall Ash in 1966, the study of generalized Riemann
derivative draw significant attention of the mathematical community
and numerous studies where carried out since then.
One of the major areas that benefits from these developments is
the numerical analysis, as the use of generalized Riemann derivatives
leads to solving a wider class of problems that are not solvable
with the classical tools. This article studies the generalized Riemann
derivative and its properties and establishes relationships between
Riemann generalized derivative and the classical one.
The existence of classical derivative implies the existence of the
Riemann generalized derivative, and we study conditions necessary
for the generalized Riemann derivative to imply the existence of
the classical derivative. Furthermore, we provide conditions on
the generalized Riemann derivative that are sufficient for the existence
of the classical derivative.
Submitted January 10, 2013. Published March 18, 2013.
Math Subject Classifications: 26A24, 28A15.
Key Words: Riemann generalized derivative; symmetric derivative;
Schwarz derivative; (sigma,tau) differentiable function.
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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 |
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Petrus Alexandrescu Institute of Sociology, Casa Academiei Romane Calea 13 Septembrie, no. 13, Bucharest 5, RO-050711, Romania email: alexandrescu_petrus@yahoo.com |
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Diana-Olimpia Alexandrescu Department of Mathematics, University of Craiova 200585 Craiova, Romania email: alexandrescudiana@yahoo.com |
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