Search

Catalan sequence initially introduced by Euler but named after Eugene Catalan has found abundant applications in the fields of probability theory, number theory, analysis, combinatorics etc. Recently ˙Ilkhan formulated the matrix associated with Catalan numbers and studied its domain in c0(C~) and c(C~). In this paper, by employing Catalan matrix defined by Catalan sequence and convergence via ideal, we establish Catalan sequence spaces c I 0 (C~), c I (C~) and ℓ I ∞(C~), study the properties of these corresponding spaces and establish inclusion relations. [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]

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]

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]

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 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 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]

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]

The concepts of statistical convergence and strong p-Cesaro summability of sequences of real numbers were introduced in literature independently, and it was shown that if a sequence is strongly p-Cesaro summable, then it is statistically convergent and also a bounded statistically convergent sequence must be p-Cesaro summable. In the present paper, two new concepts named statistical convergence of order β , γ and strongly p-Cesàro summability of order β , γ are introduced for sequences of fuzzy numbers, where α and β real numbers such that 0 < α ≤ β ≤ 1 and some relations between statistical convergence of order β , γ and strongly p-Cesàro summability of order β , γ are given. Furthermore, it is shown that a bounded and statistically convergent sequence of fuzzy numbers need not strongly p-Cesàro summable of order β , γ in general for 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 this paper, we introduce the concepts of statistically convergent sequences of order β and statistically Cauchy sequences of order β in fuzzy normed spaces. Furthermore, we give the relations between statistically convergent sequences of order β and statistically Cauchy sequences of order β. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to introduce and examine the concepts of deferred statistical convergence of order β and strong r-deferred Cesáro summability of order β for sequences of fuzzy numbers and give some relations between deferred statistical convergence sequences of order β and strongly r-deferred Cesáro summable sequences of order β, where β ∈ (0, 1] and p ∈ ℝ +. Mathematics Subject Classification: 40A05, 40C05, 46A45, 03E72. [ABSTRACT FROM AUTHOR]

In the present paper, we introduce the concept of lacunary statistical boundedness of order β for sequences of fuzzy numbers and give some relations between lacunary statistical boundedness of order β and statistical boundedness. [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]

Fuzzy set theory has entered into a large variety of disciplines of sciences, technology and humanities having established itself as an extremely versatile interdisciplinary research area. Accordingly different notions of fuzzy structure have been developed such as fuzzy normed linear space, fuzzy topological vector space, fuzzy sequence space etc. While reviewing the literature in fuzzy sequence space, we have seen that the notion of Tauberian theorems for the Euler-Nörlund mean-convergent sequences of fuzzy numbers has not been developed. In the present paper, we introduce some new concepts about statistical convergence of sequences of fuzzy numbers. The main purpose of this paper is to study Tauberian theorems for the Euler-Nörlund mean-convergent sequences of fuzzy numbers and investigate some other kind of convergences named Euler-Nörlund mean-level convergence so as to fill up the existing gaps in the literature. The results which we obtained in this study are much more general than those obtained by others. [ABSTRACT FROM AUTHOR]

In this study, using the generalized difference operator Δm, we introduce the concepts of (Δm; I)-lacunary statistical convergence of order α and lacunary strong Δmp-summability of order α of sequences and give some relations about these concepts. [ABSTRACT FROM AUTHOR]

In this paper, using the difference operator of order m and a lacunary sequence $$\theta = (k_{r})$$ , we introduce and examine some classes of sequences of fuzzy numbers. Furthermore, we study some of their properties like completeness, solidity, symmetricity and convergence free. We also give some inclusion relations related to these classes. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce and examine the concept of lacunary statistical boundedness of order α and give the relations between statistical boundedness and lacunary statistical boundedness of order α. [ABSTRACT FROM AUTHOR]

In this paper we introduce the concepts of uniform and pointwise Δm – statistical convergence of order α of sequence of functions. We also give notions of uniform and pointwise Δm – statistically Cauchy sequence of order α of sequence of functions and show that pointwise Δm – statistically Cauchy sequence (uniform Δm – statistical convergence) is equivalent to pointwise Δm – statistical convergence (uniform Δm – statistically Cauchy sequence) of order α. Moreover, some relations between pointwise Δm – statistical convergence of order α and strongly pointwise Δqm – Cesàro summable of order α of sequence of functions are given. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new type of almost statistical convergence of generalized difference sequences of fuzzy numbers involving lacunary sequences. We give the relations between the lacunary strongly almost Cesàro type convergence and lacunary almost statistical convergence. Furthermore, we study some of their properties like completeness, solidity, symmetricity etc. We also give some inclusion relations related to these classes. [ABSTRACT FROM AUTHOR]

The main purpose of this article is to introduce the concepts of almost λr-statistical convergence and strongly almost λr-convergence of order β of sequences of fuzzy numbers with respect to an Orlicz function. We give some relations between strongly almost λr-convergence and almost λr-statistical convergence of order β of sequences of fuzzy numbers. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and examine the concept of $$\lambda $$ -statistical boundedness of order $$\beta $$ of sequences of fuzzy numbers and give some relations between statistical boundedness and $$\lambda $$ -statistical boundedness of order $$\beta $$ . [ABSTRACT FROM AUTHOR]

n this paper we introduce the concepts of Wijsman ρ-statistical convergence of order α and Wijsman strongly ρ-convergence of order α. In addition, some inclusion theorems are also presented. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of pointwise statistical convergence of order α of sequences of fuzzy mappings. Furthermore we give the concept of α-statistically Cauchy sequence for sequences of fuzzy mappings and prove that it is equivalent to pointwise statistical convergence of order α of sequences of fuzzy mappings. Also some relations between Sβ(F)-statistical convergence and strong wpα) F)-summability are given. [ABSTRACT FROM AUTHOR]

We introduce and examine the concepts of Δ min(λ) ‑ asymptotic statistical equivalence of order &$945;, and strong Δ min(λ) ‑ asymptotic equivalence of order α of sequences. Also, we give some relations connected to these concepts. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept ... -- statistical convergence of order α. Also some relations between ... -statistical convergence of order α and strong ... -summability of order β are given. Furthermore some relations between the spaces ... and ... are examined. [ABSTRACT FROM AUTHOR]