Matrix transformation on statistically convergent sequence spaces of interval number sequences (original) (raw)
On Some Properties of Interval Matrices
2007
By using a new set of arithmetic operations on interval numbers, we discuss some arithmetic properties of interval matrices which intern helps us to compute the powers of interval matrices and to solve the system of interval linear equations. Keywords—Interval arithmetic, Interval matrix, linear equations.
A note on checking regularity of interval matrices
Linear and Multilinear Algebra, 1995
It is proved that two previously known sufficient conditions for regularity of interval matrices are equivalent in the sense that they cover the same class of interval matrices.
A new sequence space and matrix transformations
Thai Journal of Mathematics
The main purpose of this paper is to define the sequence space bs(p,s)and determine the necessary and sufficient conditions on the matrix sequence A = (A i ) in order that A ∈ (X, Y ), where X = l ∞ (p, s), bs(p, s) and Y = l ∞ , f, bs, f s.These results are more general than those of Lascarides and Maddox[6],Basar Solak[3],Nanda[10] and Solak .
Matrix Transformations on Some Difference Sequence Spaces
IOSR Journal of Mathematics, 2013
The sequence spaces ∞ (, , ∆), 0 (, , ∆) and (, , ∆) were recently introduced. The matrix classes (, , ∆ :) and (, , ∆ : ∞) were characterized. The object of this paper is to further determine the necessary and sufficient conditions on an infinite matrix to characterize the matrix classes (, , ∆ ∶) and (, , ∆ ∶). It is observed that the later characterizations are additions to the existing ones.
A New Sufficient Condition for Regularity of Interval Matrices
We present a sufficient regularity condition for interval matrices which generalizes two previously known ones. It is formulated in terms of positive definiteness of a certain point matrix, and can also be used for checking positive definiteness of interval matrices. Comparing it with Beeck's strong regularity condition, we show by counterexamples that none of the two conditions is more general than the other one. Above: logo of interval computations and related areas (depiction of the solution set of the system [2, 4]x 1 + [−2, 1]x 2 = [−2, 2], [−1, 2]x 1 + [2, 4]x 2 = [−2, 2] (Barth and Nuding [1])).
On some difference sequence spaces of interval numbers
Proyecciones (Antofagasta)
In this paper we introduce the sequence spaces c 0 i (∆) ,c i (∆) and i ∞ (∆) of interval numbers and study some of their algebraic and topological properties. Also we investigate some inclusion relations related to these spaces.
λ-Sequence Spaces of Interval Numbers
Applied Mathematics & Information Sciences, 2014
In this paper we introduce and study the concepts of strongly λ-convergence and statistically λ-convergence for interval numbers. We give some relations related to these concepts. The results are more general than the Mursaleen's results in [5].
On Relation Between P-Matrices and Regularity of Interval Matrices
Springer Proceedings in Mathematics & Statistics, 2017
We explore new results between P-matrix property and regularity of interval matrices. In particular, we show that an interval matrix is regular in and only if some special matrices constructed from its center and radius matrices are P-matrices. We also investigate the converse direction. We reduce the problem of checking P-matrix property to regularity of a special interval matrix. Based on this reduction, novel sufficient condition for a P-matrix property is derived, and its strength is inspected. We also state a new observation to interval P-matrices.
Some matrix transformations on analytic sequence spaces
Pacific Journal of Mathematics, 1975
Let A denote the space of all complex sequences a such that if z is a complex number and \z\ < 1 then Σ a n z n converges, and B the space of all complex sequences b for which there is a complex number z such that | z \ > 1 and Σ b n z n converges. In this paper we characterize matrix transformations from A to B and from B to A.
Regular matrix of interval numbers based on Fibonacci numbers
Afrika Matematika, 2014
The main purpose of this paper is to introduce the criterion for the regularity of a matrix whose elements are interval numbers and define a regular matrixF of interval numbers using fibonacci numbers and to introduce some new sequence spaces c i 0 (F), c i (F), l i ∞ (F) based on the newly defined regular matrix of interval numbersF and investigate some relations related to these spaces.
On full-rank interval matrices
Numerical Analysis and Applications, 2014
For interval matrices, the paper considers the problem of determining whether a matrix has full rank. We propose a full-rank criterion that relies on the search for diagonal dominance as well as criteria based on pseudoinversion of the midpoint matrix and comparison of the midpoint and the radius matrices for the interval matrix under study.
Some matrix transformations and almost convergence
Kathmandu University Journal of Science, Engineering and Technology, 2013
The sequence space bv(u,p) has been defined and the classes (bv(u,p):l?), (bv(u,p):c),and (bv(u,p):c0) of infinite matrices have been characterized by Ba?ar, Altay and Mursaleen ( see, [2] ). The main purposes of the present paper is to characterize the classes (bv(u,p):ƒ?),(bv(u, p):ƒ), and (bv(u,p):ƒ0), where ƒ?, ƒ, and ƒ0 denotes the spaces of almost bounded sequences, almost convergent sequences and almost convergent null sequences, respectively, with real or complex terms. Kathmandu University Journal of Science, Engineering and Technology Vol. 8, No. II, December, 2012, 89-92 DOI: http://dx.doi.org/10.3126/kuset.v8i2.7330
Proyecciones (Antofagasta), 2014
Recently Savas and Das [12] introduced the notion of I-statistical convergence of sequences of real numbers. In this article we introduced the sequence spaces W I(S) (M, A, p), W I(S) 0 (M, A, p) and W I(S) ∞ (M, A, p) of real numbers defined by I-statistical convergence using sequences of Orlicz function.We study some basic topological and algebraic properties of these spaces. We investigate some inclusion relations involving these spaces.
The application domain of difference type matrix D(r,0,s,0,t) on some sequence spaces
Yugoslav Journal of Operations Research, 2021
In this paper we introduce new sequence spaces with the help of domain of matrix D(r, 0, s, 0, t), and study some of their topological properties. Further, we determine β and γ duals of the new sequence spaces and finally, we establish the necessary and sufficient conditions for characterization of the matrix mappings.