In this note a mean value theorem for continuous vector functions is introduced by mollified derivatives and smooth approximations

The class of strongly semicontinuous functions is considered. For these functions the notion of mollified derivatives, introduced by Ermoliev, Norkin and Wets, is extended to the second order. By means of a generalized Taylor's formula, second order necessary and sufficient conditions are proved...

In this paper some new contractive operators on C (a,b) of IFS type are built. Inverse problems are introduced and studied by convex optimization problems. A stability result and some optimality conditions are given.

In this work we provide a characterization of Ck,1 functions on Rn (that ik K times differentiable with locally Lipschitz k-th derivatives) by means of (k+1)-th divided differences and Riemann derivatives. In particular we prove that the class of Ck,1 functions is equivalent to the class of...

In this paper we survey some notions of generalized derivative for C 1,1 functions. Furthermore some optimality conditions and numerical methods for nonlinear minimization problems involving C1,1 data are studied.

In this work we provide a characterization of C 1,1 functions on Rn (that is, differentiable with locally Lipschitz partial derivatives) by means of second directional divided differences. In particular, we prove that the class of C 1,1 functions is equivalent to the class of functions with...