Search

The main purpose of this article is to introduce the concepts of almost lacunary statistical convergence and strongly almost lacunary convergence of order (β,γ) of sequences of fuzzy numbers with respect to an Orlicz function. We give some relations between strongly almost lacunary convergence and almost lacunary statistical convergence of order (β,γ) of sequences of fuzzy numbers, where β and γ are two fixed real numbers such that 0<β≤γ≤1. [ABSTRACT FROM AUTHOR]

In this work, a new generalization of statistical boundedness is provided for difference sequences in regard to lacunary α-density and lacunary statistical sense. Apart from examining some inclusion theorems on related sequence spaces, we show that... does not form a sequence algebra unlike .... [ABSTRACT FROM AUTHOR]

In the paper, neutrosophic statistical analysis of temperature data of different cities in the southeastern Anatolia region of Turkey is given. The neutrosophic mean and neutrosophic coefficient of variation are computed using the temperature data. From the analysis, it is concluded that the temperatures of Mardin and Şanlıurfa cities are more consistent than the other cities in Turkey. In addition, the neutrosophic results are compared with results under classical statistics. Based on the comparative study, it can be concluded that neutrosophic statistical results are more adequate, flexible, and more informative than classical statistics. [ABSTRACT FROM AUTHOR]

In this study, we present a new cryptosystem named Deoxyribose Nucleic Acid (DNA) secret writing with the Laplace transform of the Mittag-Leffler function. The method is proper for encrypting large files. In this technique, we consider the original message as binary sequence. These binary streams corresponding to the plain text is transformed to DNA bases by utilizing DNA encoding, then the DNA codes are transformed to positive integers. We apply the Laplace transform to these numbers which are coefficients of the expansion of the Mittag-Leffler function. To provide multi-stage protection, the outcome coefficients are transformed to binary sequences and other level of encryption with cumulative XOR is applied and equivalent MSBs obtained at every iteration are utilized for building cipher text. Decryption is implemented in the opposite way. We employ monobit test, correlation analysis for measuring the reliability of encryption and Python programming language to obtain secret message, the plain text and computations of statistical tests. [ABSTRACT FROM AUTHOR]

In this study, the concepts of lacunary (H , 1) − summability of order α , lacunary strongly harmonic summability of order α , lacunary statistical logarithmic convergence of order α of sequences of real numbers are introduced and relations between these concepts are investigated. [ABSTRACT FROM AUTHOR]

We develop some new sequence spaces p (P (q)) and ∞ (P (q)) by using q-Pascal matrix P (q). We discuss some topological properties of the newly defined spaces, obtain the Schauder basis for the space p (P (q)) and determine the Alpha-(α -), Beta-(β -) and Gamma-(γ -) duals of the newly defined spaces. We characterize a certain class ( p (P (q)) , X) of infinite matrices, where X ∈ { ∞ , c , c 0 } . Furthermore, utilizing the proposed results, we characterize certain other classes of infinite matrices. We also examine some geometric properties, like the approximation property, Dunford–Pettis property, Hahn–Banach extension property, and Banach–Saks-type p property of the spaces p (P (q)) and ∞ (P (q)) . [ABSTRACT FROM AUTHOR]

In this article, we introduce the concepts of Wijsman deferred statistical convergence and Wijsman strong deferred Cesaro summability for double sequences of sets. Additionally, some properties and based results have been established under a few restrictions. [ABSTRACT FROM AUTHOR]

In this paper, the concept of a strongly lacunary convergence of order α in the neutrosophic normed spaces is introduced. A few fundamental properties of this new concept are investigated. [ABSTRACT FROM AUTHOR]

In this paper, we define the sequence spaces ℓ p (F ^ q) 1 ≤ p < ∞ , ℓ ∞ (F ^ q) , c 0 (F ^ q) and c (F ^ q) by using q-Fibonacci band matrix F ^ q defined by F ^ q = F ^ nk (q) = - F n + 1 (q) - 1 q n F n (q) , k = n - 1 F n + 2 (q) - 1 q n F n (q) , k = n 0 , otherwise (k , n ∈ N). We study some topological properties and give some inclusion relations for these spaces. In addition, we build a bases for the space ℓ p (F ^ q) , compute α -, β -, γ - duals of the same space, characterize some matrix classes and examine some geometric properties. [ABSTRACT FROM AUTHOR]

Study of difference sequences is a recent development in the summability theory. Sometimes a situation may arise that we have a sequence at hand and we are interested in sequences formed by its successive differences and in the structure of these new sequences. Studies on difference sequences were introduced in the 1980s and after that many mathematicians studied these kind of sequences and obtained some generalized difference sequence spaces. In this study, we generalize the concepts of weighted statistical convergence and weighted [Np]-summability of real (or complex) numbers sequences to the concepts of m-weighted statistical convergence of order a and weighted x Np a- (m, r)-summability of order a by using generalized difference operator m and examine the relationships between m-weighted statistical convergence of order a and weighted x Np a- (m, r)-summability of order a. Our results are more general than the corresponding results in the existing literature. [ABSTRACT FROM AUTHOR]

In this paper, we introduce pointwise (f, λ)-statistical convergence of order a and strong pointwise (V, f, λ)-summability of order a of sequences of fuzzy mappings. In addition, we examined some inclusion theorems among these concepts. [ABSTRACT FROM AUTHOR]

It is well-known that Paranormed spaces have more general properties than normed spaces. Until recently, the concept of paranorm has not been considered with the set of fuzzy numbers and there are no studies in literatüre from this point of view. So, our main aim in this work is to apply this notion to the set of fuzzy numbers and give the new concepts of fuzzy paranorm and fuzzy paranormed space. In addition, we discuss in detail the statistical convergence and statistically Cauchy sequence in a fuzzy paranormed space. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and examine the concept of deferred statistical boundedness of order α and give the relation between statistical boundedness and deferred statistical boundedness of order α. Apart from studying the Köthe-Toeplitz duals of S p , q α (b) , the space of deferred statistically bounded sequences of order α, a decomposition theorem is also established. Finally we give a general description of inclusion between two deferred α − statistical methods of boundedness. [ABSTRACT FROM AUTHOR]

In this article, we introduce and investigate the concepts of Δθm‐asymptotically statistical equivalent of order α˜ and strong Δθm‐asymptotically equivalent of order α˜ of double sequences. Also, we give some relationships related to these concepts. [ABSTRACT FROM AUTHOR]

The main purpose of this work is to introduce and examine the concept of (λ,f)-statistical boundedness of order α and give the relations between some known concepts and (λ,f)-statistical boundedness of order α. [ABSTRACT FROM AUTHOR]

In this paper, we introduce Fibonacci backward difference operator F Δ B l of fractional order l by the composition of Fibonacci band matrix F and difference operator Δ B l of fractional order l, defined by (Δ B l x) s = ∑ i = 0 ∞ (− 1) i Γ (l + 1) i ! Γ (l − i + 1) x s − i and introduce sequence spaces ℓ k (F Δ B l) and ℓ ∞ (F Δ B l). We present some topological properties, obtain Schauder basis and determine α -, β - and γ -duals of the spaces ℓ k (F Δ B l) and ℓ ∞ (F Δ B l). We characterize certain classes of matrix mappings from the spaces ℓ k (F Δ B l) and ℓ ∞ (F Δ B l) to any of the space ℓ ∞ , c , c 0 or ℓ 1. Finally we compute necessary and sufficient conditions for a matrix operator to be compact on the spaces ℓ k (F Δ B l) and ℓ ∞ (F Δ B l). [ABSTRACT FROM AUTHOR]

In this study, by using definition of ρ-statistical convergence which was defined by Çakallı [5], we introduce the concepts of pointwise wρα(f)-summability, pointwise ρ-statistical convergence of order α and uniform ρ-statistical convergence of order α sequences of real-valued functions. Also, we give some inclusion relations between these concepts. [ABSTRACT FROM AUTHOR]

The main object of this article is to introduce the concepts of (f, ρ)− statistical convergence of order α and strong (f, ρ)− summability of order α of sequences of real numbers and give some inclusion relations between these spaces. [ABSTRACT FROM AUTHOR]

We introduce the -statistical monotone and the -statistical order convergent sequences in Riesz spaces. We also give some relations between the lattice operations and the -statistical convergence in Riesz spaces, and also, some relations between the order convergence and -statistical order convergence. [ABSTRACT FROM AUTHOR]

In this study, we introduce deferred statistical convergence and strongly deferred Cesàro summability on an arbitrary time scale. Moreover, we examine some relationship between deferred statistical convergence and strongly deferred Cesàro summability on time scales. [ABSTRACT FROM AUTHOR]

Statistical convergence is an active area, and it appears in a wide variety of topics. However, it has not been studied extensively in Riesz spaces. There are a few studies about the statistical convergence on Riesz spaces, but they only focus on the relationship between statistical and order convergences of sequences in Riesz spaces. In this paper, we introduce the notion of (V, λ)-order summable by using the concept of λ-statistical monotone and the λ-statistical order convergent sequences in Riesz spaces. Moreover, we give some relations between (V, λ)-order summable and λ-statistical order convergence. [ABSTRACT FROM AUTHOR]

In this work, the notion of Δm−statistical boundedness is generalized with respect to α−density and λ−statistical sense. Besides some inclusion theorems regarding the new sequence spaces Δm(Sbα), Δλm(Sb) and Δλm(Sbα) are examined. [ABSTRACT FROM AUTHOR]

In this study, using the generalized difference operator Δmn, we introduce the concept of strong Δmn‐deferred Cesàro summability of order β of real sequences and investigate some topological properties its. Additionally, we give some inclusion relations about this concept. [ABSTRACT FROM AUTHOR]

In this paper, we propose to investigate a new weighted statistical convergence by applying the Nörlund–Cesáro summability method. Based upon this definition, we prove some properties of statistically convergent sequences and a kind of the Korovkin type theorems. We also study the rate of the convergence for this kind of weighted statistical convergence and a Voronovskaya type theorem. [ABSTRACT FROM AUTHOR]

In this article we introduce and examine the concepts of Δ v m (f) − statistical convergence of order α and strong Δ v m (f) − Cesàro summability of order α , and give some relations between Δ v m (f) − statistical convergence of order α and strong Δ v m (f) − Cesàro summability of order α. [ABSTRACT FROM AUTHOR]

In this study, we introduce and examine the concept of weighted statistical convergence of order α in paranormed spaces. Also some relations between weighted statistical convergence of order α and [(N, pn), g]rα -summability are given. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to introduce the concept of strongly ideal lacunary quasi-Cauchyness of sequences of real numbers. Strongly ideal lacunary ward continuity is also investigated. Interesting results are obtained. [ABSTRACT FROM AUTHOR]

The main objective of this article is to introduce the concepts of f-lacunary statistical convergence of order α and strong f-lacunary summability of order α of double sequences and give some inclusion relations between these concepts. [ABSTRACT FROM AUTHOR]

In this paper, we have introduced and examined the concepts of Δm-pointwise and Δm-uniform statistical convergence of order ... for double sequences of real valued functions. Also, we have given the concept of Δm-statistically Cauchy sequence for double sequences of real valued functions and proven that it is equivalent to Δm-pointwise statistical convergence of order for double sequences of real valued functions. Some relations between ... (Δm, f)-statistical convergence and strong ... (Δm, f)-summability have also been given. [ABSTRACT FROM AUTHOR]

We give definition of (λ, ν) statistical convergence on a product time scale. Furthermore, we generalize de la Vallée Poussin mean and define strongly (V, λ, ν) and [V, λ, ν]Ψp2_summable functions, statistical limit superior and inferior on a product time scale. Then, a few inclusion relations are expressed between the sets of (V, λ, ν) summable, p_strongly [V, λ, ν]Ψp2_summable and (λ, ν) statistical convergent functions. Furthermore, some theorems are proved related to statistical limit superior and inferior on a product time scale. [ABSTRACT FROM AUTHOR]