Die Iteration als Fundamentalprocess mathematischer Operationen.
It is proved that real functions on which can be represented as the difference of two semiconvex functions with a general modulus (or of two lower -functions, or of two strongly paraconvex functions) coincide with semismooth functions on (i.e. those locally Lipschitz functions on for which and for each ). Further, for each modulus , we characterize the class of functions on which can be written as , where and are semiconvex with modulus (for some ) using a new notion of...
In this article, we formalize in the Mizar system [3] the notion of the derivative of polynomials over the field of real numbers [4]. To define it, we use the derivative of functions between reals and reals [9].
In this paper we consider the nonlocal (nonstandard) Cauchy problem for differential inclusions in Banach spaces x'(t) ∈ F(t,x(t)), x(0)=g(x), t ∈ [0,T] = I. Investigation over some multivalued integrals allow us to prove the existence of solutions for considered problem. We concentrate on the problems for which the assumptions are expressed in terms of the weak topology in a Banach space. We recall and improve earlier papers of this type. The paper is complemented...
The main result of this paper is that if f is n-convex on a measurable subset E of ℝ, then f is n-2 times differentiable, n-2 times Peano differentiable and the corresponding derivatives are equal, and except on a countable set. Moreover is approximately differentiable with approximate derivative equal to the nth approximate Peano derivative of f almost everywhere.