Introducing a higher order modulus of smoothness based on qintegers, in this paper first we obtain Jackson-type estimates in approximation by Jackson-type generalizations of the q-Picard and q-Gauss-Weierstrass singular integrals and give their global smoothness preservation property with respect to the uniform norm. Then, we study approximation and geometric properties of the complex variants ...

We consider a real-valued path; it is possible to associate a tree to this path, and we explore the relations between the tree, the properties of p-variation of the path, and integration with respect to the path. In particular, the fractal dimension of the tree is estimated from the variations of the path, and Young integrals with respect to the path, as well as integrals from the rough paths t...

In the cumulative prospect theory (CPT) the preference (utility functional) is represented by the difference of two Choquet integrals. We investigate representations of the corresponding functional by two fuzzy integrals, specially the difference representations of the asymmetric Choquet integral with respect to a signed fuzzy measure with bounded chain variation. We discuss non-monotone, real ...

We present an algorithm to evaluate multiloop Feynman integrals with arbitrary number of internal massive lines, the masses being in general complex-valued, and its implementation \textsc{Mathematica} package \textsc{SeaSyde}. The solves by series expansions system differential equations satisfied Master Integrals. At variance respect other existing codes, analytical continuation solution is pe...

A natural generalization of (classical) measures are monotone set valued functions, the so called non-additive measures. Further generalization of measures are intervalvalued measures and interval-valued non-additive measures. Since interval-valued ⊕-measures, as a special case of intervalvalued non-additive measures, have been extensively applied in the mathematical representation of the vario...

We combine a maximum principle for vector-valued mappings established by D’Ottavio, Leonetti and Musciano [DLM] with regularity results from [BF3] and prove the Hölder continuity of the first derivatives for local minimizers u: Ω → RN of splitting-type variational integrals provided Ω is a domain in R2. Roughly speaking, anisotropic variational integrals ∫ Ω F (∇u) dx with integrand F (∇u) of (...

The natural BMO (bounded mean oscillation) conditions suggested by scalar-valued results are known to be insufficient for the boundedness of operator-valued paraproducts. Accordingly, singular integrals has only been available under versions classical “T(1)?BMO” assumptions that not easily checkable. Recently, Hong, Liu and Mei (J. Funct. Anal. 2020) observed situation improves remarkably with ...