Sezgisel fuzzy normlu uzaylarda ℐ-lacunary istatiksel yakınsaklık

In this study, first, we investigate the notions of ℐ-lacunary statistical convergence and strongly ℐlacunary convergence with regards to the intuitionistic fuzzy norm (IFN for short) (μ,ν). Then, we investigate relationships among this new concepts and make important observations about them. Futhermore, we examine the relations among ℐ-lacunary statistical convergence and ℐ-statistical convergence in terms of IFN (μ,ν) in the corresponding intuitionistic fuzzy normed space.Bu çalışmada, ilk olarak (μ,ν) sezgisel normuna göre ℐ-lacunary istatistiksel yakınsaklık ve kuvvetli ℐlacunary yakınsaklık kavramları tanımlandı. Daha sonra bu kavramlar arasındaki ilişkiler incelendi ve bu kavramlar üzerine önemli gözlemler yapıldı. Bununla birlikte, ilgili sezgisel fuzzy normlu uzayda (μ,ν) sezgisel normuna göre ℐ-lacunary istatistiksel yakınsaklık ile ℐ-istatistiksel yakınsaklık arasındaki ilişkiler incelendi

ON GENERALIZED STATISTICAL CONVERGENCE OF DOUBLE SEQUENCES VIA IDEALS IN INTUITIONISTIC FUZZY NORMED SPACES

In this paper, we introduce the concept of I₂-lacunary statistical convergence and strongly I₂-lacunary convergence with respect to the intuitionistic fuzzy norm (μ,v), investigate their relationship, and make some observations about these classes. We mainly examine the relation between these two new methods and the relation between I₂-statistical convergence in the corresponding intuitionistic fuzzy normed space

Fibonacci Lacunary Statistical Convergence In Intuitionistic Fuzzy Normed Linear Spaces

We investigate the concept of Fibonacci lacunary statistical convergence in intuitionistic fuzzy normed linear spaces. We also introduce here a new concept, that is, Fibonacci lacunary statistical completeness and show that every intuitionistic fuzzy normed linear space is Fibonacci lacunary statistically complete

I-Cesàro summability of sequences of sets

In this paper, we defined concept of Wijsman I-Cesàro summability for sequences of sets and investigate the relationships between the concepts of Wijsman strongly I-Cesàro summability, Wijsman strongly I-lacunary summability, Wijsman p-strongly I-Cesàro summability and Wijsman I-statistical convergenc

ON LACUNARY CONVERGENCE IN CREDIBILITY SPACE

In this paper, we present the notions of lacunary statistically convergent sequence for fuzzy variables, lacunary statistically Cauchy sequence in credibility space, and present a kind of lacunary statistical completeness for credibility space. Also, we present lacunary strong convergence concepts of sequences of fuzzy variables of different types

(R1958) On Deferred Statistical Convergence of Fuzzy Variables

In this paper, within framework credibility theory, we examine several notions of convergence and statistical convergence of fuzzy variable sequences. The convergence of fuzzy variable sequences such as the notion of convergence in credibility, convergence in distribution, convergence in mean, and convergence uniformly virtually certainly via postponed Cesàro mean and a regular matrix are researched using fuzzy variables. We investigate the connections between these concepts. Significant results on deferred statistical convergence for fuzzy variable sequences are thoroughly investigated

ON SOME GENERALIZED DEFERRED STATISTICAL CONVERGENCE OF ORDER αβ FOR FUZZY VARIABLE SEQUENCES IN CREDIBILITY SPACE

In this paper, we investigate the concepts of deferred statistical convergence of order αβ and strongly s-deferred Cesaro summability of order αβ for fuzzy variable sequences in credibility space. Furthermore, the conditions of deferred statistical convergence almost surely of order αβ, deferred statistical convergence in credibility of order αβ, deferred statistical convergence in mean of order αβ, deferred statistical convergence in distribution of order αβ, and deferred statistical convergence uniformly almost surely of order αβ of fuzzy variable sequences have been examined. We have proved relations between these notions

New Sequence Spaces with Respect to a Sequence of Modulus Functions

In this paper, we introduce the notions of  -invariant convergence, -invariant convergence with respect to a sequence of modulus functions and establish some basic theorems. Furthermore, we give some properties of   -Cauchy sequence and   -Cauchy sequence. We basically study some connections between -invariant statistical convergence and  -invariant lacunary statistical convergence with respect to a sequence of modulus functions and between strongly  -invariant convergence and  -invariant lacunary statistical convergence with respect to a sequence of modulus functions. Also, we establish some inclusion relations between new concepts of  statistically convergence and  –invariant statistically convergence with respect to a sequence of modulus functions

On I_{σ}-convergence of folner sequence on amenable semigroups

In this paper, the concepts of-uniform density of subsetsAof the setof positive integers and corresponding-convergence of functions defined on discrete countable amenable semigroups were introduced. Furthermore, for any Folner sequenceinclusion relations between-convergence and invariant convergence also-convergence andVp-convergence were given. Weintroduce the concept of-statisticalconvergence and-lacunary statisticalconvergence of functions defined on discrete countableamenable semigroups. In addition to these definitions, we give some inclusion theorems. Also, we make a new approach to the notionsofV-summability,-convergence and-statistical convergence of Folner sequences by using ideals and introduce new notions,namely,-V-summability,--statisticalconvergence of Folner sequences. We mainly examine the relation between these twomethods as also the relation between-statistical convergence and--statistical convergence of Folner sequences introduced bythe author recently