New Classes of Statistically Pre-Cauchy Triple Sequences of Fuzzy Numbers Defined by Orlicz Function

2018 ◽  
Vol 85 (3-4) ◽  
pp. 411
Author(s):  
Sangita Saha ◽  
Santanu Roy
Keyword(s):  
Cauchy Sequence ◽  
Fuzzy Numbers ◽  
Orlicz Function ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Real Numbers ◽  
Fuzzy Real Numbers ◽  
Sequences Of Fuzzy Numbers ◽  
Necessary And Sufficient

In this article, the concept of statistically pre-Cauchy sequence of fuzzy real numbers having multiplicity greater than two defined by Orlicz function is introduced. A characterization of the class of bounded statistically pre-Cauchy triple sequences of fuzzy numbers with the help of Orlicz function is presented. Then a necessary and suffcient condition for a bounded triple sequence of fuzzy real numbers to be statistically pre-Cauchy is proved. Also a necessary and sufficient condition for a bounded triple sequence of fuzzy real numbers to be statistically convergent is derived. Further, a characterization of the class of bounded statistically convergent triple sequences of fuzzy numbers is presented and linked with Cesaro summability.

scholarly journals Generalized Nörlund and Nörlund-type Means of Sequences of Fuzzy Numbers

2020 ◽  
Vol 13 (5) ◽  
pp. 1088-1096
Author(s):  
Pradosh Kumar Pattanaik ◽  
Susanta Kumar Paikray ◽  
Bidu Bhusan Jena
Keyword(s):  
Fuzzy Numbers ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Slow Oscillation ◽  
Real Numbers ◽  
Fuzzy Real Numbers ◽  
Sequences Of Fuzzy Numbers ◽  
Necessary And Sufficient ◽  
Convergent Sequences

In this article we study some properties of generalized Nörlund and Nörlund-typemeans of sequences of fuzzy real numbers. We establish necessary and sufficient conditions for our purposed methods to transform convergent sequences of fuzzy real numbers into convergent sequences of fuzzy real numbers which also preserve the limit. Finally, we establish some results showing the connection between the generalized N ̈orlund and N ̈orlund-type limits and the usual limits under slow oscillation of sequences of fuzzy real numbers.

scholarly journals On some spaces of Cesàro sequences of fuzzy numbers associated with λ-convergence and Orlicz function

2019 ◽  
Vol 11 (1) ◽  
pp. 156-171
Author(s):  
K. Raj ◽  
S. Pandoh
Keyword(s):  
Fuzzy Numbers ◽  
Orlicz Function ◽  
Sequence Spaces ◽  
Real Numbers ◽  
Inclusion Relations ◽  
Algebraic Properties ◽  
Fuzzy Real Numbers ◽  
Sequences Of Fuzzy Numbers

Abstract In the present paper we shall introduce some generalized difference Cesàro sequence spaces of fuzzy real numbers defined by Musielak-Orlicz function and -convergence. We make an e ort to study some topological and algebraic properties of these sequence spaces. Furthermore, some inclusion relations between these sequence spaces are establish.

scholarly journals A characterization theorem for levelwise statistical convergence

Filomat ◽  
2011 ◽  
Vol 25 (1) ◽  
pp. 133-143 ◽  
Author(s):  
Salih Aytar
Keyword(s):  
Cauchy Sequence ◽  
Statistical Convergence ◽  
Fuzzy Numbers ◽  
Characterization Theorem ◽  
Bounded Sequence ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Statistical Cluster ◽  
Necessary And Sufficient ◽  
Cluster Points

In the present paper, we prove a characterization theorem which gives a necessary and sufficient condition for a sequence of fuzzy numbers to be levelwise statistically convergent in the space of fuzzy numbers. As an application of this theorem we utilize the idea of statistical equi-continuity in order to obtain a condition which guarantees the set of levelwise statistical cluster points of a statistically bounded sequence to be nonempty and a levelwise statistically Cauchy sequence to be levelwise statistically convergent.

On representation of Poisson mixtures as Poisson sums and a characterization of the gamma distribution

1977 ◽  
Vol 82 (2) ◽  
pp. 297-300 ◽  
Author(s):  
A. V. Godambe
Keyword(s):  
Gamma Distribution ◽  
Exponential Type ◽  
Similar Condition ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Poisson Mixture ◽  
Mixing Distribution ◽  
Poisson Mixtures ◽  
Necessary And Sufficient

AbstractA necessary and sufficient condition for a Poisson mixture with an exponential type mixing distribution to be equivalently represented as a Poisson sum is obtained. The problem of deriving a similar condition under any mixing distribution on (0, ∞) is discussed. Finally, a characterization of the gamma distribution is obtained.

A characterization of the Poisson process

1974 ◽  
Vol 11 (1) ◽  
pp. 72-85 ◽  
Author(s):  
S. M. Samuels
Keyword(s):  
Poisson Process ◽  
Renewal Process ◽  
Poisson Processes ◽  
Renewal Processes ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Complete Proof ◽  
Necessary And Sufficient

Theorem: A necessary and sufficient condition for the superposition of two ordinary renewal processes to again be a renewal process is that they be Poisson processes.A complete proof of this theorem is given; also it is shown how the theorem follows from the corresponding one for the superposition of two stationary renewal processes.

On weak convergence within the hnbue family of life distributions

1984 ◽  
Vol 21 (03) ◽  
pp. 654-660 ◽  
Author(s):  
Sujit K. Basu ◽  
Manish C. Bhattacharjee
Keyword(s):  
Weak Convergence ◽  
Exponential Distribution ◽  
Limiting Distribution ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Moment Sequence ◽  
Positive Order ◽  
Life Distributions ◽  
Necessary And Sufficient

We show that the HNBUE family of life distributions is closed under weak convergence and that weak convergence within this family is equivalent to convergence of each moment sequence of positive order to the corresponding moment of the limiting distribution. A necessary and sufficient condition for weak convergence to the exponential distribution is given, based on a new characterization of exponentials within the HNBUE family of life distributions.

A continuous generalization of the transversal property

1984 ◽  
Vol 95 (1) ◽  
pp. 21-23
Author(s):  
P. Komjáth
Keyword(s):  
Finite Subset ◽  
Measure Space ◽  
Choice Function ◽  
Finite Measure ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Finite Sets ◽  
Real Numbers ◽  
One To One ◽  
Necessary And Sufficient

A transversal for a set-system is a one-to-one choice function. A necessary and sufficient condition for the existence of a transversal in the case of finite sets was given by P. Hall (see [4, 3]). The corresponding condition for the case when countably many countable sets are given was conjectured by Nash-Williams and later proved by Damerell and Milner [2]. B. Bollobás and N. Varopoulos stated and proved the following measure theoretic counterpart of Hall's theorem: if (X, μ) is an atomless measure space, ℋ = {Hi: i∈I} is a family of measurable sets with finite measure, λi (i∈I) are non-negative real numbers, then we can choose a subset Ti ⊆ Hi with μ(Ti) = λi and μ(Ti ∩ Ti′) = 0 (i ≠ i′) if and only if μ({U Hi: iεJ}) ≥ Σ{λi: iεJ}: for every finite subset J of I. In this note we generalize this result giving a necessary and sufficient condition for the case when I is countable and X is the union of countably many sets of finite measure.

A characterization of the exponential distribution

1972 ◽  
Vol 9 (02) ◽  
pp. 457-461 ◽  
Author(s):  
M. Ahsanullah ◽  
M. Rahman
Keyword(s):  
Probability Distribution ◽  
Order Statistics ◽  
Lebesgue Measure ◽  
Random Variable ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Positive Random Variable ◽  
Absolutely Continuous ◽  
Necessary And Sufficient

A necessary and sufficient condition based on order statistics that a positive random variable having an absolutely continuous probability distribution (with respect to Lebesgue measure) will be exponential is given.

A dynamical characterization of diagonal-preserving -isomorphisms of graph -algebras

2017 ◽  
Vol 38 (7) ◽  
pp. 2401-2421 ◽  
Author(s):  
SARA E. ARKLINT ◽  
SØREN EILERS ◽  
EFREN RUIZ
Keyword(s):  
Directed Graphs ◽  
Sufficient Condition ◽  
Orbit Equivalence ◽  
Necessary And Sufficient Condition ◽  
Graph Algebras ◽  
Boundary Path ◽  
Necessary And Sufficient

We characterize when there exists a diagonal-preserving $\ast$-isomorphism between two graph $C^{\ast }$-algebras in terms of the dynamics of the boundary path spaces. In particular, we refine the notion of ‘orbit equivalence’ between the boundary path spaces of the directed graphs $E$ and $F$ and show that this is a necessary and sufficient condition for the existence of a diagonal-preserving $\ast$-isomorphism between the graph $C^{\ast }$-algebras $C^{\ast }(E)$ and $C^{\ast }(F)$.

Comparison of density topologies on the real line

2018 ◽  
Vol 68 (1) ◽  
pp. 173-180
Author(s):  
Renata Wiertelak
Keyword(s):  
Real Line ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Real Numbers ◽  
The Real ◽  
Closed Intervals ◽  
The Family ◽  
Necessary And Sufficient

Abstract In this paper will be considered density-like points and density-like topology in the family of Lebesgue measurable subsets of real numbers connected with a sequence 𝓙= {Jn}n∈ℕ of closed intervals tending to zero. The main result concerns necessary and sufficient condition for inclusion between that defined topologies.

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