Paper's Title:

Integrability of Sine and Cosine Series Having Coefficients of a New Class

Author(s):

L. Leindler

Abstract:

Some integrability theorems or only their sufficient part are generalized such that the coefficients of the sine and cosine series belong to a new class of sequences being wider than the class of sequences of rest bounded variation, which itself is a generalization of the monotone decreasing sequences, but a subclass of the almost monotone decreasing sequences. It is also verified that the new class of sequences and the class of almost monotone decreasing sequences are not comparable.

Paper's Title:

Necessary and Sufficient Conditions for Uniform Convergence and Boundedness of a General Class of Sine Series

Author(s):

Laszlo Leindler

Bolyai Institute, University of Szeged,
Aradi Vértanúk tere 1,
H-6720 Szeged,
Hungary.
leindler@math.u-szeged.hu

Abstract:

For all we know theorems pertaining to sine series with coefficients from the class γGBVS give only sufficient conditions. Therefore we define a subclass of γGBVS in order to produce necessary and sufficient conditions for the uniform convergence and boundedness if the coefficients of the sine series belong to this subclass; and prove two theorems of this type.

Paper's Title:

On the Degree of Approximation of Continuous Functions that Pertains to the Sequence-To-Sequence Transformation

Author(s):

Xhevat Z. Krasniqi

University of Prishtina,
Department of Mathematics and Computer Sciences,
5 Mother Teresa Avenue, Prishtinë, 10000,
Republic of Kosovo.
 

xheki00@hotmail.com

Abstract:

In this paper we prove analogous theorems like Leindler's 3 using the so-called A-transform of the B-transform of the partial sums of Fourier series. In addition, more than two such transforms are introduced and for them analogous results are showed as well.

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:

An Application of Quasi Power Increasing Sequences

Author(s):

Hüseyín Bor

Department of Mathematics, Erciyes University, 38039 Kayseri, Turkey
bor@erciyes.edu.tr
Url: Http://math.erciyes.edu.tr/Hbor.htm

Abstract:

In this paper a result of Bor [2] has been proved under weaker conditions by using a -quasi power increasing sequence instead of an almost increasing sequence.

Paper's Title:

Some Generalized Difference Sequence Spaces Defined by Orlicz Functions

Author(s):

Ramzi S. N. Alsaedi and Ahmad H. A. Bataineh

Department of Mathematics, King Abdul Aziz University,
Jeddah P.O.Box 80203,
Saudia Arabia
ramzialsaedi@yahoo.co.uk

Department of Mathematics, Al al-Bayt University,
Mafraq 25113,
Jordan
ahabf2003@yahoo.ca

Abstract:

In this paper, we define the sequence spaces: [V,M,p,u,Δ ],[V,M,p,u,Δ]₀ and [V,M,p,u,Δ]_∞, where for any sequence x=(x_n), the difference sequence Δx is given by Δx=(Δx_n) = (x_n-x_n-1) . We also study some properties and theorems of these spaces. These are generalizations of those defined and studied by Savas and Savas and some others before.

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