JFS
Journal of Function Spaces
2314-8888
2314-8896
Hindawi Publishing Corporation
178042
10.1155/2014/178042
178042
Editorial
Matrix Transformations, Measures of Noncompactness, and Applications
Mohiuddine
S. A.
1
Banaś
Józef
2
Mursaleen
M.
3
Patterson
Richard F.
4
http://orcid.org/0000-0001-7780-8137
Alotaibi
Abdullah
1
http://orcid.org/0000-0002-6656-113X
Aghajani
Asadollah
5
1
Department of Mathematics
Faculty of Science
King Abdulaziz University
P.O. Box 80203
Jeddah 21589
Saudi Arabia
kau.edu.sa
2
Department of Mathematics
Rzeszów University of Technology
Al. Powstańców Warszawy 8
35-959 Rzeszów
Poland
prz.edu.pl
3
Department of Mathematics
Aligarh Muslim University
Aligarh 202 002
India
amu.ac.in
4
Department of Mathematics and Statistics
University of North Florida
Building 14
Jacksonville
FL 32224
USA
unf.edu
5
School of Mathematics
Iran University of Science and Technology
P.O. Box 16846-13114
Tehran
Iran
iust.ac.ir
2014
1352014
2014
27
02
2014
27
02
2014
13
5
2014
2014
Copyright © 2014 S. A. Mohiuddine et al.
This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The significance of the theory of matrix transformations has been strikingly demonstrated in various contexts, for example, in Fourier analysis, analytic continuation, quantum mechanics, probability theory, and approximation theory. Also the theory of matrix transformations on one hand and measures of noncompactness on the other hand are successfully linked to obtain necessary and sufficient conditions for matrix maps between certain sequence spaces of a general class to be compact operators. Recently, these results on compact matrix operators have become a useful tool in the study of infinite system of differential and integrodifferential equations in sequence spaces.
The paper of Y. Liang et al. is concerned with the existence of positive solutions for the initial value problem of fractional evolution equation with noncompact semigroup in a Banach space.
The paper of M. Ertürk and V. Karakaya presents also existence of n-tuplet coincidence points in the framework of intuitionistic fuzzy normed space.
The issue contains also two papers related to approximation theory. The paper by A. Alotaibi et al. is devoted to study the Korovkin type approximation theorem for periodic functions of two variables by using the notion of statistical summability (C,1,1). The second paper, written by M. A. Alghamdi, applies the notion of σ-convergence to obtain Korovkin type approximation theorem for function of two variables. The author of that paper constructs an example in support of his result by considering classical Bernstein polynomials of two variables.
The paper by V. Karakaya and F. Altun, which we are going to describe briefly, discusses some basic properties of the modular on the space ℓρΔ(u,v,p). The authors of that paper investigated some relationships between the modular and the Luxemburg norm on ℓρΔ(u,v,p) and also studied some geometric properties on this space.
Finally, the paper written by F. Gürsoy and V. Karakaya used Kirk multistep-SP and Kirk-S iterative algorithms to obtain some convergence and stability results.
S.A. Mohiuddine
Józef Banas
M. Mursaleen
Richard F. Patterson
Abdullah Alotaibi
Asadollah Aghajani