In this paper we give a survey about recent versions of Korovkin-type theorems for modular function spaces, class which includes $L^p$, Orlicz, Musielak-Orlicz spaces and many others. We consider various kinds convergence, using certain summability processes, like triangular matrix statistical filter convergence (which are generalizations the convergence). Finally, wwe an abstract axiomatic pre...

...........................................................................................................................v List of Figures ..................................................................................................................viii List of Tables ...................................................................................................................x Chapt...

We study the general problem of oblique projections in discrete shift-invariant spaces of 12 and we give error bounds on the approximation. We define the concept of discrete multiresolutions and wavelet spaces and show that the oblique projections on certain subclasses of discrete multiresolutions and their associated wavelet spaces can be obtained using perfect reconstruction filter banks. The...

The purpose of this paper is to introduce and study regular bopen sets (briefly rb-open sets) in topological spaces and obtain some of their properties. We introduce the rb-closure and discuss some basic properties of the rb-closure. Also we study the new concepts of rb-closed spaces by means of filter bases. Mathematics Subject Classification: 54A05, 54A20

ـــــ In [25], we introduce the notion of r-fuzzy neighborhood filters in smooth topological spaces in sense of Gähler [10], and used it to define and study separation axioms , = , , . Here we continue our study of the axioms of separation in smooth topological spaces. Therefore, we introduce the notion of r-fuzzy neighborhood filter at a set. Then by using this notion we define and study separ...

In this paper we begin to develop the filter approach to (completeness of) quasiuniform spaces, proposed in [8, Section V]. It will be seen that this permits a more powerful and elegant account of completion to be given than was feasible using sequences or nets [8]. Just as in the previous version [8], we find that received notions concerning convergence need to be revised and reformulated to d...

This paper describes a new packet filter mechanism that efficiently dispatches incoming network packets to one of multiple endpoints, for example address spaces. Earlier packet filter systems iteratively applied each installed filter against every incoming packet, resulting in high processing overhead whenever multiple filters existed. Our new packetfilter provides an associative match function...

Topological sequential spaces are the fixed points of a Galois correspondence between collections of open sets and sequential convergence structures. The same procedure can be followed replacing open sets by other topological concepts, such as closure operators or (ultra)filter convergences. The fixed points of these other Galois correspondences are not topological spaces in general, but they c...