


Paper's Title:
Integrability of Sine and Cosine Series Having Coefficients of a New Class
Author(s):
L. Leindler
Bolyai Institute,
University of Szeged, Aradi Vértanúk Tere 1, H6720 Szeged, Hungary
leindler@math.uszeged.hu
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,
H6720 Szeged,
Hungary.
leindler@math.uszeged.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 SequenceToSequence Transformation
Author(s):
Xhevat Z. Krasniqi
University of Prishtina,
Department of Mathematics and Computer Sciences,
5
Mother Teresa Avenue, Prishtinë, 10000,
Republic of Kosovo.
Abstract:
In this paper we prove analogous theorems like Leindler's 3 using the socalled Atransform of the Btransform 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.
Email: xhevat.krasniqi@unipr.edu
URL:
https://staff.unipr.edu/profile/xhevatkrasniqi
Abstract:
In this paper, for the first time, we introduce the deferred matrix means which contain the wellknown 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 alBayt 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_{n1}) . 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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