The adjoints of differentiable mappings

On distribution functions of the derivatives of weakly differentiable mappings

The Convenient Setting for Non-quasianalytic Denjoy–carleman Differentiable Mappings

For Denjoy–Carleman differential function classes C where the weight sequence M = (Mk) is logarithmically convex, stable under derivations, and non-quasianalytic of moderate growth, we prove the following: A mapping is C if it maps C -curves to C -curves. The category of C -mappings is cartesian closed in the sense that C (E, C (F, G)) = C (E × F, G) for convenient vector spaces. Applications t...

The Convenient Setting for Quasianalytic Denjoy–carleman Differentiable Mappings

For quasianalytic Denjoy–Carleman differentiable function classes C where the weight sequence Q = (Qk) is log-convex, stable under derivations, of moderate growth and also an L-intersection (see (1.6)), we prove the following: The category of C-mappings is cartesian closed in the sense that C(E,C(F,G)) ∼= C(E × F,G) for convenient vector spaces. Applications to manifolds of mappings are given: ...

Hermite-hadamard Type Inequalities for the Product Two Differentiable Mappings

In this paper we extend some estimates of the right hand side of a Hermite-Hadamard type inequality for the product two differentiable functions whose derivatives absolute values are convex. Some natural applications to special weighted means of real numbers are given. Finally, an error estimate for the Simpson’s formula is also addressed.

On the Existence of Right Adjoints for Surjective Mappings between Fuzzy Structures

We continue our study of the characterization of existence of adjunctions (isotone Galois connections) whose codomain is insufficiently structured. This paper focuses on the fuzzy case in which we have a fuzzy ordering ρA on A and a surjective mapping f : 〈A,≈A〉 → 〈B,≈B〉 compatible with respect to the fuzzy equivalences ≈A and ≈B . Specifically, the problem is to find a fuzzy ordering ρB and a ...