Paper's Title:

On Trigonometric Approximation of Continuous Functions by Deferred Matrix Means

Author(s):

Xhevat Zahir Krasniqi

Faculty of Education,
University of Prishtina "Hasan Prishtina",
Avenue "Mother Theresa " no. 5, Prishtinë 10000,
Republic of Kosovo.
E-mail: xhevat.krasniqi@uni-pr.edu
URL: https://staff.uni-pr.edu/profile/xhevatkrasniqi

Abstract:

In this paper, for the first time, we introduce the deferred matrix means which contain the well-known generalized deferred Nörlund, deferred Nörlund, deferred Riesz, deferred Cesàro means introduced earlier by others, and a new class of sequences (predominantly a wider class than the class of Head Bounded Variation Sequences). In addition, using the deferred matrix means of Fourier series of a continuous function, we determine the degree of approximation of such function via its modulus of continuity and a positive mediate function.

Paper's Title:

A relation between nuclear cones and full nuclear cones

Author(s):

G. Isac and A. B. Nemeth

Department of Mathematics,
Royal Military College of Canada,
P. O. Box 17000 STN Forces Kingston, Ontario,
Canada K7K 7B4.
isac-g@rmc.ca

Faculty of Mathematics and Computer Science,
Babes-Bolyai University,
3400 Cluj-Napoca,
Romania.
nemab@math.ubbcluj.ro

Abstract:

The notion of nuclear cone in locally convex spaces corresponds to the notion of well based cone in normed spaces. Using the bipolar theorem from locally convex spaces it is proved that every closed nuclear cone is a full nuclear cone. Thus every closed nuclear cone can be associated to a mapping from a family of continuous seminorms in the space to the topological dual of the space. The relation with Pareto efficiency is discussed.

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