n this paper, we consider continuity properties(especially, regularity, also viewed as an approximation property) for $%mathcal{p}_{0}(x)$-valued set multifunctions ($x$ being a linear,topological space), in order to obtain egoroff and lusin type theorems forset multifunctions in the vietoris hypertopology. some mathematicalapplications are established and several physical implications of thema...

We consider the problem of minimizing the distance ‖f − φ‖Lp(K), where K is a subset of the complex unit circle ∂D and φ ∈ C(K), subject to the constraint that f lies in the Hardy space H(D) and |f | ≤ g for some positive function g. This problem occurs in the context of filter design for causal LTI systems. We show that the optimization problem has a unique solution, which satisfies an extrema...

When dealing with large amounts of data, exact query answering is not always feasible. We propose a query approximation method that, given an upper bound on the amount of data that can be used (i.e., for which query evaluation is still feasible), identifies a part C of the data D that (i) fits in the available space budget; and (ii) provides accurate query results. That is, for a given query Q,...

A reproducing kernel Hilbert space restricts the space of functions to smooth functions and has structure for function approximation and some aspects in learning theory. In this paper, the solution of an integral equation of the third kind is constructed analytically using a new method. The analytical solution is represented in the form of series in the reproducing kernel space. Some numerical ...

The purpose of this paper is to discuss the degree best monotone multi- approximation unbounded functions weighted space in terms modules smoothness by using some algebraic linear operators. In addition, introduced ,proofs properties modulus smoothness.

In this paper, three types of (philosophical, optimistic and pessimistic) multigranulation single valued neutrosophic (SVN) covering-based rough set models are presented, and these three models are applied to the problem of multi-criteria group decision making (MCGDM).Firstly, a type of SVN covering-based rough set model is proposed.Based on this rough set model, three types of mult...