
Rabia SavaşIstanbul Medeniyet University · Mathematics and education
Rabia Savaş
Assoc. Prof.
About
48
Publications
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Introduction
Publications
Publications (48)
The purpose of this article is to present the concepts of double statistical convergence in credibility and [Formula: see text]-double statistical convergence in credibility in pringsheim sense. By using these definitions we present a natural multidimensional extension of Credibility theory via Summability methods.
Connor and Savas (Acta Math Hung 145:416–432, 2015) presented the concept of sliding window method. The main purpose of this article is to extend Connor and Savas results to higher dimension. To accomplish this we define a new summability method for multidimensional measurable real valued functions defined on \([0,\infty )\times [0,\infty )\). Addi...
In 1971, the definition of Orlicz $\widetilde{\phi}$ functions was introduced by Lindenstrauss and Tzafriri and moreover in 2006, the notion of double lacunary sequences was presented by Savaş and Patterson. The primary focus of this article is to introduce the double statistically $\widetilde{\phi }$-convergence and double lacunary statistically $...
Kurzweil and Henstock presented the notion of Gauge integral, independently. Using their definition Savas and Patterson examined the relationship between Gauge integral and Summability theory. Because of the esoteric of both Gauge and Summability theory, the body of literature is limited. As such the only accessible notion to both theories is Pring...
In 1932 Agnew presented the concept of deferred Cesáro means. Following Agnew’s results, Küçükaslan and Yılmaztürk introduced the definition of deferred statistical convergence for sequences. Also, Patterson studied the notion of asymptotically equivalent sequences. In 2020, Savas generalized Patterson’s definition for measurable functions by consi...
The main goal of this article is to present the notion of double asymptotically lacunary statistical equivalent of order α for sequences of fuzzy numbers by considering fuzzy numbers and Pringsheim limit. To accomplish this goal, we mainly investigate some fundamental properties of the newly introduced notion. Additionally, it should be note that s...
In 2019, Mursaleen and Mohiuddine introduced the concept of lacunary statistical convergence for sequences on intuitionistic fuzzy normed spaces. The goal of this article is to present Mursaleen and Mohiuddine’s work into the class of nonnegative real-valued functions. To achieve this, we present the notion of sliding window methods for measurable...
In this paper, we introduce new definitions which are related to the notions \(\lambda \mu\)–double asymptotically statistically equivalent to multiple L and strongly \(\lambda \mu\)–double asymptotically equivalent to multiple L by using \(f(\varsigma ,\tau )\) and \(g(\varsigma ,\tau )\) bivariate measurable real valued functions on \(\left( 1,\i...
The concept of fuzzy metric spaces was presented by George and Veeramani in 1994. Following their results, Gregori and Romaguera examined some properties of fuzzy metric spaces in 2000. On the other hand, the idea of statistical convergence was introduced by Fast in 1951 and this concept was extended for double sequences by Mursaleen and Moricz in...
The primary purpose of this article is to introduce double deferred invariant statistical convergence and double strongly invariant convergence for double sequences. Additionally, some implications are examined.
The primary goal of this article is to present the concepts of asymptotically equivalent function and asymptotic regular function transformations. Moreover, by using these definitions, we examine the bivariate function transformation of asymptotically statistical equivalent measurable functions.
In 1971, Chow and Teicher presented a probability approximation Theorem via summability methods. The goal of this article is to extend Chow and Teicher results to higher dimension. To achieve this we consider multidimensional totally monotonic and independent identically random variables. Using these notions we present a series of approximation typ...
The goal of this article is to present double almost lacunary statistical convergence of weight of g in 2-normed spaces. Furthermore, we examine some inclusion theorems and variations.
The concept of P-convergent double sequence spaces was presented in 1988 by Moricz and Rhoades, and also in 2005, the notion of almost lacunary strongly P-convergent double sequences was introduced by Savas and Patterson, using Orlicz functions. Following these two concepts, we present the double almost lacunary strongly P-convergent of weight g vi...
During the late 50's and early 60's, the notion of Gauge integral was presented by Kurzweil and Henstock, independently. The purpose of this paper is to extend this concept to Summability theory. To accomplish this, we introduce the notion of γ−strongly summable to L with respect to Gauge by using h(ϑ) measurable real valued function defined on (1,...
In this article, we present a topological result by considering the generalization of lacunary almost p-bounded variation sequence spaces. Additionally, some matrix transformations have been discussed.
The goal of this paper includes the generalization of the notions of \left[
V,\lambda ,\mu \right] (\mathcal{I}_{2})-double strongly summability and
\mathcal{I}_{2}-\lambda \mu -$double statistical convergence by taking
nonnegative real-valued Lebesgue measurable two dimensional functions on
\left( 1,\infty \right) \times \left( 1,\infty \right) $...
The primary target of this article is to introduce a new summability sequence space 𝑆𝜆,𝜇−𝜙˜. In addition, we will present some of its properties and examine some interesting results by using double statistically 𝜙˜ ‐convergence, [𝐶,1,1]𝜙˜ ‐ summability, and [𝑉,𝜆,𝜇]𝜙˜ ‐summability, which are new summability methods.
One of the wide-ranging applications and research areas of Summa-bility theory is the concept of statistical convergence. This concept was studied a related concept of convergence by using lacunary sequence by Fridy and Orhan. In the last quarter of the 20th century, lacunary statistical convergence has been discussed and captured significant aspec...
The aim of this article is to consider almost lacunary statistical convergence of order θ for double sequences and is to present some inclusion theorems.
In 1932 Agnew [1] introduced the concept of deferred Ces´aro means.
Taking inspiration from this new approach, in this paper we introduce deferred
asymptotically equivalent sequences using statistical convergence and prove some
important results. This will be accomplished through a series of regularity type
theorems.
Let I2 ? P(N ? N) be a nontrivial ideal. We provide a new approach to the concept of I2-double lacunary statistical convergence and I2-lacunary strongly double summable by taking f(?,?), which is a multidimensional measurable real valued function on (1,?) ? (1,?). Additionally, we examine the relation between these two new methods.
In this paper, by using a nonnegative real-valued Lebesque measurable function in the interval \(\left( 1,\infty \right) \) we introduce the concepts of strong \((V, \lambda ,p)\)-summability and \(\lambda \)-statistical convergence of weight \(g : [0, \infty ) \rightarrow [0, \infty )\) where \(g(x_n) \rightarrow \infty \) for any sequence \((x_n)...
In 1964 Borwein presented functional characterization of the normed linear spaces wp and Wp. These two spaces are clearly linked to Cesàro summability [C, 1] in particular it should be noted that a sequence x in wp if and only if x is Cesàro summable. The goal of this paper includes extension of these notions to double function space thus producing...
We introduce new definitions related to the notions of asymptotically λ
I
λ
-statistical equivalent of order \alpha to multiple L and strongly λ
I
λ
-asymptotically equivalent of order α
α
to multiple L
L
by using two nonnegative real-valued Lebesque measurable functions in the interval (1,∞)
(
1
,
∞
)
instead of sequences. In addition, we also p...
1933, Adams [1] developed Hausdorff
transformations for double sequences. H. Şevli and R. Savas [18] proved some result for double Endl- Jakimovski (E-J) generalization. In this study, we consider some further results for E-J Hausdorff transformations for double sequences.
In this paper, we study the definition and basic results on $\lambda$-
double strongly summable and $\lambda$- double statistically convergence
from functions of one variable to real valued functions measurable on $%
\left( 1,\infty \right) \times \left( 1,\infty \right) $
The goal of this article is to study I2−equivalence double nonnegative sequences. To accomplish this we present a series of theorems that are similar to the following: If A is a nonnegative four dimensional summability matrix that maps bounded double sequences to ℓ2 and let I2 and J2 be admissible ideals in N×N then the following are equivalent.
•...
In (Savaş in Indian J Math 56(2):1–10 (2014) [27]), we examine the asymptotically \(\mathcal {I}^{\lambda }\)-statistical equivalent of order \(\alpha \) which is a natural combination of the definition for asymptotically equivalent of order \(\alpha \), where \(0 < \alpha \le 1\), \(\mathcal {I}\)-statistically limit, and \(\lambda \)-statistical...
Das (Proc. Camb. Philos. Soc. 67:321-326, 1970) proved that every conservative Hausdorff matrix is absolutely kth power conservative. Savaş and Rhoades (Anal. Math. 35:249-256, 2009) proved the result of Das for double Hausdorff summability. In this paper we will consider the double Endl-Jakimovski (E-J) generalization and we will prove the corresp...