Diferenciální počet II [Book]
Difference of general integral means.
Difference properties of higher orders for continuity and Riemann integrability
Differences of Decreasing Slowly Varying Functions
Differences of two semiconvex functions on the real line
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...
Differences of weighted mixed symmetric means and related results.
Different aspects of differentiability [Book]
Differentation along algebras.
Differentiability from the representation formula and the Sobolev-Poincaré inequality
In the geometries of stratified groups, we provide differentiability theorems for both functions of bounded variation and Sobolev functions. Proofs are based on a systematic application of the Sobolev-Poincaré inequality and the so-called representation formula.
Differentiability of Minima of Non-Differentiable Functionals.
Differentiability of Polynomials over Reals
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].
Differentiability points of a distance function
Differentiable Functions into Real Normed Spaces
In this article, we formalize the differentiability of functions from the set of real numbers into a normed vector space [14].
Differentiable Functions on Normed Linear Spaces
In this article, we formalize differentiability of functions on normed linear spaces. Partial derivative, mean value theorem for vector-valued functions, continuous differentiability, etc. are formalized. As it is well known, there is no exact analog of the mean value theorem for vector-valued functions. However a certain type of generalization of the mean value theorem for vector-valued functions is obtained as follows: If ||ƒ'(x + t · h)|| is bounded for t between 0 and 1 by some constant M, then...
Differential analysis of matrix convex functions. II.
Differential conditions to verify the Jacobian Conjecture
Let F be a polynomial mapping of ℝ², F(O) = 0. In 1987 Meisters and Olech proved that the solution y(·) = 0 of the autonomous system of differential equations ẏ = F(y) is globally asymptotically stable provided that the jacobian of F is everywhere positive and the trace of the matrix of the differential of F is everywhere negative. In particular, the mapping F is then injective. We give an n-dimensional generalization of this result.
Differential estimate for -ary forms on closed orthants.
Differential inclusions and multivalued integrals
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...
Differential sandwich theorems of -valent functions associated with a certain fractional derivative operator