Bukovský, Lev
Published in
Tatra Mountains Mathematical Publications

The paper tries to survey the recent results about relationships between covering properties of a topological space X and the space USC(X) of upper semicontinuous functions on X with the topology of pointwise convergence. Dealing with properties of continuous functions C(X), we need shrinkable covers. The results are extended for A-measurable and u...

Eskandarian, Zohreh
Published in
Lobachevskii Journal of Mathematics

We consider linear normed spaces of measurable functions dominated by positive measurable function powered by real positive parameter. Also, we consider its dual and predual, and we propose a method for constructing a limit spaces of these functional spaces taken by power parameter. We prove that these limit spaces are (LF)-spaces and also prove th...

Caponetti, Diana Trombetta, Alessandro Trombetta, Giulio
Published in
Mathematica Slovaca

We define and study the moduli d(x, 𝓐, D) and i(x, 𝓐,D) related to monotonicity of a given function x of the space L0(Ω) of real-valued “measurable” functions defined on a linearly ordered set Ω. We extend the definitions to subsets X of L0(Ω), and we use the obtained quantities, d(X) and i(X), to estimate the Hausdorff measure of noncompactness γ(...

Kalmynin, A. B.
Published in
Mathematical Notes

Zakharov, V. K. Rodionov, T. V.
Published in
Mathematical Notes

It is well known that the family of all continuous functions on a topological space contains all constant functions and is closed with respect to the usual pointwise operations (addition, multiplication, finite supremum and infimum, division) and uniform convergence. The complete description of such function families (normal families) was given by ...

Bikchentaev, A. M.
Published in
Siberian Mathematical Journal

We prove the additivity of regular l-additive mappings T: → [0,+∞] of a hereditary cone in the space of measurable functions on a measure space. Some examples are constructed of non-d-additive l-additive mappings T. The monotonicity of l-additive mappings T: → [0,+∞] is established. The examples are constructed of nonmonotone d-additive mappings T....

Et, Mikail Mohiuddine, Syed Abdul Alotaibi, Abdullah
Published in
Journal of Inequalities and Applications

In this study, using the notion of (V,λ)-summability and λ-statistical convergence, we introduce the concepts of strong (V,λ,p)-summability and λ-statistical convergence of order α of real-valued functions which are measurable (in the Lebesgue sense) in the interval (1,∞). Also some relations between λ-statistical convergence of order α and strong ...

Simonov, B. V.
Published in
Mathematical Notes

For a mixed modulus of smoothness of positive order, its relationship with the norms of partial sums of a Fourier series in a mixed metric is obtained. The relation between mixed moduli of smoothness of positive order in different mixed metrics is established.

Malykhin, Yu. V.
Published in
Mathematical Notes

We study the relationship between two characteristics of functional classes, pseudodimension and bracketing entropy. (Pseudodimension is a generalization of VC-dimension to classes of functions. Bracket entropy characterizes the L1-error of one-sided approximation of a class by finite sets.) It is shown that classes of continuous functions with fin...

Kozhevnikova, L. M.
Published in
Mathematical Notes

For a wide class of domains of revolution, we construct examples of the nonuniqueness of solutions of the first mixed problem for the heat equation, which supports the exactness of a uniqueness class of Täcklind type.