the non-differentiability and implicit definition of boundary of production possibility set (pps) in data envelopment analysis (dea) are two important difficulties for obtaining directional characteristics, including different elasticity measures and marginal rates of substitution. also, imposing weight restrictions in dea models have some shortcomings and misunderstandings. in this paper we ut...

We present a second order differentiability theory for convex functions on Banach spaces.

In the traditional approach to differentiability, found in almost all university textbooks, this notion is considered only for interior points of domain function or functions with an open domain. This leads fact that differentiability has usually been Rn, which severely limits possibility applying potential techniques and tools differential calculus a broader class functions. Although there gre...

We prove a $$C^m$$ Lusin approximation theorem for horizontal curves in the Heisenberg group. This states that every absolutely continuous curve whose velocity is $$m-1$$ times $$L^1$$ differentiable almost everywhere coincides with except on set of small measure. Conversely, we show result no longer holds if differentiability replaced by approximate differentiability. shows our optimal and hig...

In this paper we use the fuzzy Caputo derivatives under generalized Hukuhara difference to introduce fuzzy fractional Volterra-Fredholm integro-differential equations and prove the existence and uniqueness of the solutions for this class of fractional equations.

We prove a Noether’s theorem for fractional variational problems with Riesz-Caputo derivatives. Both Lagrangian and Hamiltonian formulations are obtained. Illustrative examples in the fractional context of the calculus of variations and optimal control are given.