相关论文: A parallel treatment of semi-continuous functions …
We deduce mixed quasi-norm estimates of Lebesgue types on semi-continuous convolutions between sequences and functions which may be periodic or possess a weaker form of periodicity in certain directions. In these directions, the Lebesgue…
A real valued function $f$ defined on a subset $E$ of $\textbf{R}$, the set of real numbers, is statistically upward continuous if it preserves statistically upward half quasi-Cauchy sequences, is statistically downward continuous if it…
In this paper, we introduce and investigate the concepts of down continuity and down compactness. A real valued function $f$ on a subset $E$ of $\R$, the set of real numbers is down continuous if it preserves downward half Cauchy sequences,…
A real function $f$ is ward continuous if $f$ preserves quasi-Cauchyness, i.e. $(f(x_{n}))$ is a quasi-Cauchy sequence whenever $(x_{n})$ is quasi-Cauchy; and a subset $E$ of $\textbf{R}$ is quasi-Cauchy compact if any sequence…
Extended real-valued functions are often used in optimization theory, but in different ways for infimum problems and for supremum problems. We present an approach to extended real-valued functions that works for all types of problems and…
We prove that the smallest minimizer s(f) of a real convex function f is less than or equal to a real point x if and only if the right derivative of f at x is non-negative. Similarly, the largest minimizer t(f) is greater or equal to x if…
In this paper, we continue studying the properties of $\gamma$-semi-continuous and $\gamma$-semi-open functions introduced in [5].
Data with multiple functional recordings at each observational unit are increasingly common in various fields including medical imaging and environmental sciences. To conduct inference for such observations, we develop a paired two-sample…
Roughly speaking, functional analysis is the study of vector spaces of arbitrary dimension over the field of real or complex numbers, and the continuous linear mappings between such spaces. Naturally, the notion of continuity requires a…
Estimating heterogeneous treatment effects with machine learning has attracted substantial attention in both academic research and industrial practice. However, the two communities often evaluate models under markedly different conditions.…
A semi-process is an analog of the semi-flow for non-autonomous differential equations or inclusions. We prove an abstract result on the existence of measurable semi-processes in the situations where there is no uniqueness. Also, we allow…
In this paper we provide a rigorous mathematical foundation for continuous approximations of a class of systems with piece-wise continuous functions. By using techniques from the theory of differential inclusions, the underlying piece-wise…
Integrating with respect to functions which are constant on intervals whose bounds are discontinuity points (of those functions) is frequent in many branches of Mathematics, specially in stochastic processes. For such functions and alike…
The aim of this paper is to provide characterizations of the Lebesgue-almost everywhere continuity of a function f : [a, b] $\rightarrow$ R. These characterizations permit to obtain necessary and sufficient conditions for the Riemann…
We give a necessary and sufficient condition for non-local functionals on vector-valued Lebesgue spaces to be weakly sequentially lower semi-continuous. Here a non-local functional shall have the form of a double integral of a density which…
A natural connection between rational functions of several real or complex variables, and subspace collections is explored. A new class of function, superfunctions, are introduced which are the counterpart to functions at the level of…
Some concepts, such as non-compactness measure and condensing operators, defined on metric spaces are extended to uniform spaces. Such extensions allow us to locate, in the context of uniform spaces, some classical results existing in…
Properties of metrics and pairs consisting of left and right connections are studied on the bimodules of differential 1-forms. Those bimodules are obtained from the derivation based calculus of an algebra of matrix valued functions, and an…
Given a strictly positive measure, we characterize inner semicontinuous solid convex-valued mappings for which continuous functions which are selections almost everywhere are selections. This class contains continuous mappings as well as…
The present paper is focused on the computation of the Lipschitz upper semicontinuity modulus of the feasible set mapping in the context of fully perturbed linear inequality systems; i.e., where all coefficients are allowed to be perturbed.…