In this paper, we study linear fuzzy time-variant optimal control systems using the generalized differentiability concept and we present the general form of optimal controls and states. Some examples are provided to illustrate our results.

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...

Introduction. This paper contains the first unified treatment of the dual theory of differentiability of the norm functional in a real normed linear space. With this, the work of Smulian [2; 3] is extended and it is shown how uniform convexity is to be modified so as to obtain geometric properties dual to the various types of differentiability of the norm thus answering a question implicit in t...