M. Mursaleen

On the Euler sequence spaces which include the spaces l p and l ∞ I

In the present paper, we introduce the Euler sequence space ep^r consisting of all sequences whose Euler transforms of order r are in the space @?p of non-absolute type which is the BK-space including the space @?p and prove that the spaces ep^r and @?p are linearly isomorphic for 1=

Schauder Basis, Separability, and Approximation Property in Intuitionistic Fuzzy Normed Space

We define and study the concepts of Schauder basis, separability, and approximation property in intuitionistic fuzzy normed spaces and establish some results related to these concepts. We also display here some interesting examples by using classical sequence spaces l𝑝(1≤𝑝≤∞).

Infinite System of Differential Equations in Some Spaces

The first measure of noncompactness was defined by Kuratowski in 1930 and later the Hausdorff measure of noncompactness was introduced in 1957 by Goldenštein et al. These measures of noncompactness have various applications in several areas of analysis, for example, in operator theory, fixed point theory, and in differential and integral equations. In particular, the Hausdorff measure of noncompactness has been extensively used in the characterizations of compact operators between the infinite-dimensional Banach spaces. In this paper, we present a brief survey on the applications of measures of noncompactness to the theory of infinite system of differential equations in some spaces and .

Some Matrix Transformations of Convex and Paranormed Sequence Spaces into the Spaces of Invariant Means

We determine the necessary and sufficient conditions to characterize the matrices which transform convex sequences and Maddox sequences into 𝑉𝜎(𝜃) and 𝑉∞𝜎(𝜃).

Tauberian theorems for statistically convergent double sequences

In [F. Moricz, Tauberian theorems for Cesaro summable double sequences, Studia Math. 110 (1994) 83-96], Moricz has proved some Tauberian theorems for Cesaro summable double sequences and deduced the Tauberian theorems of Landau [E. Landau, Uber die Bedeutung einiger neuerer Grenzwertsatze der Herren Hardy and Axer, Prac. Mat.-Fiz. 21 (1910) 97-177] and Hardy [G.H. Hardy, Divergent Series, Univ. Press, Oxford 1956] type. In [J.A. Fridy, M.K. Khan, Statistical extension of some classical Tauberian theorems, Proc. Amer. Math. Soc. 128 (2000) 2347-2355], Fridy and Khan have given statistical extensions of some classical Tauberian theorems. The concept of statistical convergence for double sequences has recently been introduced by Mursaleen and Edely [M. Mursaleen, Osama H. H. Edely, Statistical convergence of double sequences, J. Math. Anal. Appl. 288 (2003) 223-231] and by Moricz [F. Moricz, Statistical convergence of multiple sequences, Arch. Math. 81 (2003) 82-89] independently. In this paper we give some Tauberian theorems for statistically convergent double sequences. We have also provided some examples including an example to Problem 1 of Moricz [F. Moricz, Tauberian theorems for Cesaro summable double sequences, Studia Math. 110 (1994) 83-96].

Matrix Transformations, Measures of Noncompactness, and Applications

1 Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia 2Department of Mathematics, Rzeszow University of Technology, Al. Powstancow Warszawy 8, 35-959 Rzeszow, Poland 3Department of Mathematics, Aligarh Muslim University, Aligarh 202 002, India 4Department of Mathematics and Statistics, University of North Florida, Building 14, Jacksonville, FL 32224, USA 5 School of Mathematics, Iran University of Science and Technology, P.O. Box 16846-13114, Tehran, Iran

Statistically strongly regular matrices and some core theorems

We define the statistically strongly regular matrices analogous to nthe strongly regular matrices, and further we use these matrices to establish necessary and sufficient conditions to prove some core theorems.

Rate of convergence of Chlodowsky type Durrmeyer Jakimovski-Leviatan operators

Abstract In this paper, we determine the rate of pointwise convergence of the Chlodowsky type Durrmeyer Jakimovski-Leviatan operators L*2 n(f; x) for functions of bounded variation. We use some methods and techniques of probability theory to prove our main result.

Recent Developments on Sequence Spaces and Compact Operators with Applications

The aim of this special issue is to focus on recent developments and achievements in the theory of function spaces, sequences spaces and their geometry, and compact operators and their applications in various fields of applied mathematics, engineering, and other sciences. The theory of sequence spaces is powerful tool for obtaining positive results concerning Schauder basis and plays a fundamental role in creating the basis of several investigations conducted in nonlinear analysis. The compactness is very often used in fixed point theory and its applications to the theories of differential, functional differential, integral, and integrodifferential equations. n nThe research papers in this special issue cover various topics like geometry of Banach spaces, Schauder basis and dual spaces, sequence spaces and their topological and geometric properties, approximation of positive linear operators by matrix and nonmatrix methods, convergence and stability results for iterative process, applications of iterative methods to a nonlinear integral equation, Littlewood-Paley operators on Morrey spaces, matrix transformations between certain sequence spaces, measures of noncompactness and their applications in characterizing compact matrix operators, fixed point theorems and their applications, and so on.

Korovkin type approximation theorem for functions of two variables via statistical summability (C, 1)

The concept of statistical summability (C, 1) has recently been introduced by Moricz (2002). In this paper, we use this notion of summability to prove the Korovkin type approximation theorem for functions of two variables. Finally we construct an example by Bleimann, Butzer and Hahn operators to show that our result is stronger than those of previously proved by other authors for ordinary convergence and statistical convergence.