On Differentiability with Respect to Parameters of the Lebesgue integral

Volume 3, Issue 4, 2002

Article 64

ON DIFFERENTIABILITY WITH RESPECT TO PARAMETERS OF THE LEBESGUE INTEGRAL

UNIVERSITATEA ''CONSTANTIN BRANCUSI''
BULEVARDUL REPUBLICII NR.1,
1400 TARGU-JIU, ROMANIA
E-Mail: lupulescu_v@yahoo.com

Received 07 December, 2001; Accepted 20 July, 2002.
Communicated by: S.S. Dragomir

ABSTRACT. The aim of this paper is to extend the results of [7] and [8] to a Lebesgue integral whose integrand and limits of integration depend on parameters.

[7] E.J. McSHANE, Integration, Princeton Univ.Press, 1947.
[8] I. MIRICA, Generalization Derivatives with the Applications in Optimal Control and Optimization, PhD Thesis, Univ. Iasi, 1997.

Key words:
Lebesgue integral, Contingent cones, Contingent derivatives.

2000 Mathematics Subject Classification:
Primary 49J52, 26A27, Secondary 46G05, 26A42.

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