Search

In this study, we investigate the concept of I * -statistical convergence for sequences of fuzzy numbers. We establish several theorems that provide a comprehensive understanding of this notion, including the uniqueness of limits, the relationship between I * -statistical convergence and classical convergence, and the algebraic properties of I * -statistically convergent sequences. We also introduce the concept of I * -statistical pre-Cauchy and I * -statistical Cauchy sequences and explore its connection to I * -statistical convergence. Our results show that every I * -statistically convergent sequence is I * -statistically pre-Cauchy, but the converse is not necessarily true. Furthermore, we provide a sufficient condition for an I * -statistically pre-Cauchy sequence to be I * -statistically convergent, which involves the concept of I * − l i m i n f . [ABSTRACT FROM AUTHOR]

Let D = {{ C : ||| < 1} be the open unit disk in the complex plane C and let H(D) be the space of all holomorphic functions on D. For a non-negative integer n and a function f H(D), the nthh order differentiation operator is defined as Dnf = f(n). The weighted composition operator together with nthh order differentiation operator give rise to a new operator generally termed as generalized weighted composition operator denoted by Wn, and is defined by Wn, f(() = (()f(n)(((()), f H(D); D, where H(D) and is a holomorphic self-map of D. This operator is basically the combination of multiplication operator MM, composition operator CC and nthh order differentiation operator Dn. We study the boundedness and compactness of this operator between Dirichlet-type spaces and Bloch-type spaces. [ABSTRACT FROM AUTHOR]

The central objective of this paper is to investigate the lacunary statistical convergence of order γ and strong lacunary summability of order γ for sequences of fuzzy functions by using the modulus function and a regular matrix. We examine the relevant inclusion relations between these spaces under specific conditions. Additionally, we study properties related to these spaces and establish several interesting results. [ABSTRACT FROM AUTHOR]

In this paper, for fuzzy metric spaces we will attempt to demonstrate some novel fixed-point theorems that is common. To support our findings with evidence, we employ the concept of compatibility. The previous review found several useful mutual fixedpoint theorems for metric and fuzzy metric spaces. Our results greatly expand and strengthen these theorems. Reconsideration of fuzzy metric spaces is done by this study so that fuzzy scalars are utilized to construct fuzzy metric spaces rather than real numbers or fuzzy numbers. In contrast to the preceding work, which defined fuzzy metric spaces using fuzzy or real numbers, this definition uses fuzzy numbers. It has been demonstrated that any complete regular metric space can, under certain conditions, complete fuzzy metric space are given. In addition, we provide evidence that the fuzzy metric spaces generate fuzzy topology that is specified in this study and is consistent with previously presented fuzzy topologies. In the coming years, these findings will pave the way for additional research into imperfect optimization and pattern recognition. [ABSTRACT FROM AUTHOR]

The current study aims to investigate the notion of set sequences in the context of fuzzy anti-norm linear space. We define the fuzzy α-anti Wijsman convergence, fuzzy α-anti Wijsman statistical convergence, and fuzzy α-anti Hausdorrf statistical convergence, for 0 < α< 1, and presented some novel examples to support the definitions. Additionally, some original theorems which show how the notions are connected, are established. [ABSTRACT FROM AUTHOR]

We generalized the concepts in the probability of rough lacunary statistical analysis of order η by introducing the difference operator A of fractional order, where a is a proper fraction and y = (Ymnk) is any fixed sequence of nonzero real or complex numbers. We study some properties of this operator involving lacunary sequence and arbitrary sequence p = (prst) of strictly positive real numbers and investigate the topological structures of related with triple difference sequence spaces. The main focus of the present paper is to generalize rough lacunary statistical analysis of order n of triple difference sequence spaces and give the relations between statistical analysis and lacunary statistical analysis of order n. [ABSTRACT FROM AUTHOR]

In the present paper we introduce some sequence spaces using ideal convergence and Musielak-Orlicz function M = (Mk) over n-normed spaces. We also examine some topolog ical properties of the resulting sequence spaces. [ABSTRACT FROM AUTHOR]

In this article we introduce the Riesz difference sequence space rpq(ΔBα) of fractional order α, defined by the composition of fractional backward difference operator ΔBα given by (ΔBαv)k = ... and the Riesz matrix Rq. We give some topological properties, obtain the Schauder basis and determine the α-, β- and γ- duals and investigate certain geometric properties of the space rpq(ΔBα). Finally, we characterize certain classes of compact operators on the space rpq(ΔBα) using Hausdorff measure of non-compactness. [ABSTRACT FROM AUTHOR]

In this paper, we introduce triple sequence spaces via Orlicz function and examine some properties of the resulting these spaces. [ABSTRACT FROM AUTHOR]

In this study, we introduce the concept of triple interval valued sequence space l3(p), where p=(puvw) is a triple sequence of bounded strictly positive numbers and study its different properties like completeness, solidness, converge free etc. We prove some inclusion relations also. [ABSTRACT FROM AUTHOR]

In this article, we introduce the class of p-absolutely summable fuzzy real valued double sequence (2lp)Fθ We have studied some algebraic properties like solid, symmetric, convergence free, sequence algebra. Further, we establish some relation with the class of p-Cesàro summable double sequences and some other important inclusion results.

In this paper we study the concept of asymptotically double lacunary statistical convergent sequences in probabilistic normed spaces and prove some basic properties.

Triple sequence convergence has an extremly important position in the basic theory of mathematics. The present manuscript contains four types of convergence concept of convergence almost surely, convergence incredibility, trust convergence in mean and convergence in distribution and discuss the relation ship among those and some mathematical properties of those new convergence.

We introduce and study some basic properties of Bernstein-Stancu polynomials of rough I-convergent of triple sequence spaces and also study the set of all Bernstein-Stancu polynomials of rough I-limits of a triple sequence spaces and relation between analytic ness and Bernstein-Stancu polynomials of rough I-core of a triple sequence spaces.

The fundamental concept of statistical convergence first was put forward by Steinhaus [20] and at the same time but also by Fast [14] independently both for complex and real sequences. In fact, the conver)gence in terms of statistical manner can be seen as a generalized form of the common convergence notion that is in the parallel of the theory of usual convergence. Measuring how large a subset of the set of natural number can be possible by means of asymptotic density. It is intuitively known that positive integers are in fact far beyond the fact that they are perfect squares. This is due to the fact that each perfect square is positive and besides at the same time there are many other positive integers. But it is also known that the set consisting of integers which are positive is not larger than that of those which are perfect squares: both of those sets are countable and infinite and therefore can be considered in terms of 1-to-1 correspondence. However, when the natural numbers are scanned for increasing order, then the squares are seen increasingly scarcity. It is at this point that the concept of natural density comes into out help and this intuition becomes more precise. In this study, the above mentioned statistical convergence and asymptotic density concepts are examined in a new space and an attempt is made to fill a gap in the literature as follows. Stancu type extension of the widely known Chlodowsky type (λ, q)-operators is going to be introduced. Moreover, the description of the novel rough statistical convergence having Pascal Fibonacci binomial matrix is going to be presented and several general characteristics of rough statistical convergence are taken into consideration. In the second place, the approximation theory is investigated as the rate of the rough statistical convergence of Chlodowsky type (λ, q)-operators. [ABSTRACT FROM AUTHOR]

In this short article, we discussed some difference double sequence spaces defined by Orlicz function and study different properties of these spaces and also establish some inclusion results among them. [ABSTRACT FROM AUTHOR]