Search

A quasi-metric is a distance function which satisfies the triangle inequality but is not symmetric in general. Quasi-metrics are a subject of comprehensive investigation both in pure and applied mathematics in areas such as in functional analysis, topology and computer science. The main purpose of this paper is to extend the convergence and Cauchy conditions in a quasi-metric space by using the notion of asymptotic density. Furthermore, some results obtained are related to completeness, compactness and precompactness in this setting using statistically Cauchy sequences.

The incomplete gamma function Γ(a, u) is defined by Γ(a, u) = ∫u∞ta−1e−tdt, where u > 0. Using the incomplete gamma function, we define a new Poisson like regular matrix P(μ) = (pnkμ) given by pnkμ = n! Γ(n+1, μ) e−μμkk! (0 ≤ k ≤ n), 0 (k > n), where μ > 0 is fixed. We introduce the sequence space ℓp(P(μ)) for 1 ≤ p ≤ ∞ and some topological properties, inclusion relations and generalized duals of the newly defined space are discussed. Also we characterize certain matrix classes and compact operators related to the space ℓp(P(μ)). We obtain Gurarii's modulus of convexity and investigate some geometric properties of the new space. Finally, spectrum of the operator P(μ) on sequence space c0 has been investigated. [ABSTRACT FROM AUTHOR]

In this paper, we first define a new regular matrix by using the arithmetic function called Jordan totient function and study the matrix domain of this newly introduced matrix in the Banach space ℓp. After computing the dual spaces of this new space, we characterize certain matrix mappings related to this space. [ABSTRACT FROM AUTHOR]

The necessary and sufficient conditions for compactness of a matrix operator between Banach spaces is obtained by utilizing the concept of the Hausdorff measure of noncompactness. This is one of the most interesting application in the theory of sequence spaces. In this paper, the compact operators are characterized on Jordan totient sequence spaces by using the concept of the Hausdorff measure of noncompactness. [ABSTRACT FROM AUTHOR]

Szász‐Mirakyan operators are a powerful tool that can be used to approximate functions on the unbounded interval [0,∞). In this contribution, we propose a numerical solution of Volterra integral equations with the help of Szász‐Mirakyan operators. In this direction, we provide both numerical scheme and estimation of error bound of solution. Numerical experiments are also presented, highlighting the performance of the new constructions of proposed algorithm in the context of one‐dimensional approximation. [ABSTRACT FROM AUTHOR]

In this paper, we first define a new regular matrix by using the arithmetic function called Jordan totient function and study the matrix domain of this newly introduced matrix in the Banach space ℓp. After computing the dual spaces of this new space, we characterize certain matrix mappings related to this space. [ABSTRACT FROM AUTHOR]

Copyright of Mugla Journal of Science & Technology is the property of Mugla Journal of Science & Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The main purpose of this paper is to define a new conservative matrix by means of the fascinating sequence of Catalan numbers and study the matrix domain of this newly introduced matrix in the classical sequence spaces c and c 0 . Additionally, after determining the Köthe-Toeplitz dual, generalized Köthe-Toeplitz dual and Garling dual, certain matrix transformations and compact operators are characterized on the new Banach spaces. [ABSTRACT FROM AUTHOR]

The main purpose of this manuscript is to introduce Banach spaces c 0 Φ and c Φ as the matrix domain of a regular matrix Φ derived by the Euler totient function. These spaces consist of φ -convergent to zero and φ -convergent sequences, respectively. After determining α -, β - and γ -duals of these spaces, some matrix classes are characterized. Finally, using the Hausdorff measure of noncompactness, the characterization of some classes of compact operators on the space c 0 Φ is given. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to define a new conservative matrix by means of the fascinating sequence of Catalan numbers and study the matrix domain of this newly introduced matrix in the classical sequence spaces c and c 0 . Additionally, after determining the Köthe-Toeplitz dual, generalized Köthe-Toeplitz dual and Garling dual, certain matrix transformations and compact operators are characterized on the new Banach spaces. [ABSTRACT FROM AUTHOR]

Norm of an operator T:X→Y is the best possible value of U satisfying the inequality ‖Tx‖Y≤U‖x‖X,and lower bound for T is the value of L satisfying the inequality ‖Tx‖Y≥L‖x‖X,where ‖.‖X and ‖.‖Y are the norms on the spaces X and Y, respectively. The main goal of this paper is to compute norms and lower bounds for some matrix operators from the weighted sequence space ℓp(w) into a new space called as Fibonacci weighted difference sequence space. For this purpose, we firstly introduce the Fibonacci difference matrix F˜ and the space consisting of sequences whose F˜‐transforms are in ℓp(w˜). [ABSTRACT FROM AUTHOR]

In this paper, we define a new class of s-type X(u, v; lp(E)) operators, Lu,v,E. Also we show that this class is a quasi-Banach operator ideal and we study on the properties of the classes which are produced via different types of s-numbers. [ABSTRACT FROM AUTHOR]

Copyright of Karaelmas Science & Engineering Journal / Karaelmas Fen ve Mühendislik Dergisi is the property of Karaelmas Science & Engineering Journal and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The main purpose of this paper is to define a new type of statistical convergence of sequences in a cone metric space and investigate the relations of these sequences with some other sequences. [ABSTRACT FROM AUTHOR]

Bourbaki complete metric spaces are important since they are a class between compact metric spaces and complete metric spaces. The aim of the present paper is to introduce the statistical Bourbaki-Cauchy sequence as a new concept and to give an equivalent condition for a metric space to be Bourbaki complete. Also, Bourbaki complete and Bourbaki-bounded metric spaces are characterized in terms of functions which preserve statistical Bourbaki-Cauchy sequences. [ABSTRACT FROM AUTHOR]

In this paper, the concept of (i, j)-γ-P-open sets in bitopological spaces are introduced and characterizations of their related notions are given. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notions of G-uniform continuity and G-Cauchy continuity of a function defined from one generalized metric space to another generalized metric space. Also, we investigate the relationships between these two types continuity and ordinary continuity. Further, we give some special properties of G-Cauchy sequences and G-totally bounded sets. [ABSTRACT FROM AUTHOR]

In this paper, new classes of lacunary ideal convergent and lacunary ideal bounded sequences combining an infinite matrix and an Orlicz function are defined. Some properties of these spaces are investigated and also some inclusion relations are obtained. [ABSTRACT FROM AUTHOR]

In this paper, we define new spaces as a generalization of the Fibonacci difference sequence spaces. Also, we establish some inclusion theorems related to these spaces and find the-,-,-duals. Lastly, we characterize some matrix classes on these spaces. [ABSTRACT FROM PUBLISHER]

In this paper, we define I-convergence and I*-convergence of an infinite product by Cauchy conditions and prove the relation between these two notions. [ABSTRACT FROM AUTHOR]