scholarly journals On I-statistically ϕ-convergence

2021 ◽  
Vol 40 (3) ◽  
pp. 593-604
Author(s):  
Shyamal Debnath ◽  
Chiranjib Choudhury
Keyword(s):  
Real Number ◽  
Number Sequence ◽  
Basic Properties ◽  
Limit Points ◽  
Cluster Points

In this paper we investigate the notion of I-statistical ϕ-convergence and introduce IS-ϕ limit points and IS-ϕ cluster points of real number sequence and also studied some of its basic properties.

scholarly journals On I-statistically limit points and I-statistically cluster points of sequences of fuzzy numbers

Mathematica ◽  
2021 ◽  
Vol 63 (86) (1) ◽  
pp. 140-147
Author(s):  
Binod Chandra Tripathy ◽  
Shyamal Debnath ◽  
Debjani Rakshit
Keyword(s):  
Limit Point ◽  
Fuzzy Numbers ◽  
Cluster Point ◽  
Basic Properties ◽  
Sequences Of Fuzzy Numbers ◽  
Limit Points ◽  
Cluster Points

The main aim of this paper is to introduce I-st limit points and I-st cluster points of a sequence of fuzzy numbers and also study some of its basic properties. Conditions for a I-st limit point of a I-st cluster point are investigated.

SOME PROPERTIES OF EQUIDISTRIBUTED AND WELL DISTRIBUTED SEQUENCES

2021 ◽  
Vol 10 (9) ◽  
pp. 3175-3184
Author(s):  
Leila Miller-Van Wieren
Keyword(s):  
Real Numbers ◽  
Statistical Cluster ◽  
Different Types ◽  
Limit Points ◽  
Cluster Points

Many authors studied properties related to distribution and summability of sequences of real numbers. In these studies, different types of limit points of a sequence were introduced and studied including statistical and uniform statistical cluster points of a sequence. In this paper, we aim to prove some new results about the nature of different types of limit points, this time connected to equidistributed and well distributed sequences.

scholarly journals On subsequential limit points of a sequence of iterates. II

1985 ◽  
Vol 38 (1) ◽  
pp. 118-129
Author(s):  
M. Maiti ◽  
A. C. Babu
Keyword(s):  
Continuous Function ◽  
Distance Function ◽  
Metric Space ◽  
Product Space ◽  
Topological Spaces ◽  
Limit Points ◽  
Cluster Points

AbstractJ. B. Diaz and F. T. Metcalf established some results concerning the structure of the set of cluster points of a sequence of iterates of a continuous self-map of a metric space. In this paper it is shown that their conclusions remain valid if the distance function in their inequality is replaced by a continuous function on the product space. Then this idea is extended to some other mappings and to uniform and general topological spaces.

scholarly journals Statistical limit point theorems

2000 ◽  
Vol 23 (11) ◽  
pp. 741-752 ◽  
Author(s):  
Jeff Zeager
Keyword(s):  
Complex Number ◽  
Limit Point ◽  
Statistical Convergence ◽  
Nonnegative Matrix ◽  
Bounded Sequence ◽  
Regular Matrix ◽  
Number Sequence ◽  
Statistical Limit ◽  
Limit Points

It is known that given a regular matrixAand a bounded sequencexthere is a subsequence (respectively, rearrangement, stretching)yofxsuch that the set of limit points ofAyincludes the set of limit points ofx. Using the notion of a statistical limit point, we establish statistical convergence analogues to these results by proving that every complex number sequencexhas a subsequence (respectively, rearrangement, stretching)ysuch that every limit point ofxis a statistical limit point ofy. We then extend our results to the more generalA-statistical convergence, in whichAis an arbitrary nonnegative matrix.

scholarly journals On Lacunary Mean Ideal Convergence in Generalized Randomn-Normed Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Awad A. Bakery ◽  
Mustafa M. Mohammed
Keyword(s):  
Normed Space ◽  
Complex Numbers ◽  
Normed Spaces ◽  
Ideal Convergence ◽  
Cauchy Sequences ◽  
Limit Points ◽  
Positive Integers ◽  
Cluster Points

An idealIis a hereditary and additive family of subsets of positive integersℕ. In this paper, we will introduce the concept of generalized randomn-normed space as an extension of randomn-normed space. Also, we study the concept of lacunary mean (L)-ideal convergence andL-ideal Cauchy for sequences of complex numbers in the generalized randomn-norm. We introduceIL-limit points andIL-cluster points. Furthermore, Cauchy andIL-Cauchy sequences in this construction are given. Finally, we find relations among these concepts.

ON THE FRACTIONAL PARTS OF RATIONAL POWERS

2009 ◽  
Vol 05 (06) ◽  
pp. 1037-1048 ◽  
Author(s):  
ARTŪRAS DUBICKAS
Keyword(s):  
Real Number ◽  
General Result ◽  
Rational Number ◽  
Limit Points ◽  
The Difference ◽  
New Inequalities

Let ξ be a non-zero real number, and let a = p/q > 1 be a rational number. We denote by U(a,ξ) and L(a,ξ) the largest and the smallest limit points of the sequence of fractional parts {ξ an}, n = 0,1,2,…, respectively. A possible way to prove Mahler's conjecture claiming that Z-numbers do not exist is to show that U(3/2,ξ) > 1/2 for every ξ > 0. We prove that U(3/2,ξ) cannot belong to [0,1/3) ∪ S, where S is an explicit infinite union of intervals in (1/3,1/2). This result is a corollary to a more general result claiming that, for any rational a > 1, U(a,ξ) cannot lie in a certain union of intervals. We also obtain new inequalities for the difference U(a,ξ) - L(a,ξ). Using them we show that some analogues of Z-numbers do not exist.

scholarly journals On rough convergence in 2-normed spaces and some properties

Filomat ◽  
2019 ◽  
Vol 33 (16) ◽  
pp. 5077-5086
Author(s):  
Mukaddes Arslan ◽  
Erdinç Dündar
Keyword(s):  
Normed Space ◽  
Normed Spaces ◽  
Fixed Sequence ◽  
Limit Points ◽  
Cluster Points

In this study, we investigated relationships between rough convergence and classical convergence and studied some properties about the notion of rough convergence, the set of rough limit points and rough cluster points of a sequence in 2-normed space. Also, we examined the dependence of r-limit LIMr 2xn of a fixed sequence (xn) on varying parameter r in 2-normed space

scholarly journals Wijsman Rough λ Statistical Convergence of Order α of Triple Sequence of Functions

2017 ◽  
Vol 2 (1) ◽  
pp. 07-15
Author(s):  
A. Esi ◽  
N. Subramanian ◽  
M. Aiyub
Keyword(s):  
Statistical Convergence ◽  
Sequence Spaces ◽  
Natural Density ◽  
Limit Points ◽  
Cluster Points ◽  
Sequence Of Functions

In this paper, using the concept of natural density, we introduce the notion of Wijsman rough λ statistical convergence of order α triple sequence of functions. We define the set of Wijsman rough λ statistical convergence of order α of limit points of a triple sequence spaces of functions and obtain Wijsman λ statistical convergence of order α criteria associated with this set. Later, we prove that this set is closed and convex and also examine the relations between the set of Wijsman rough λ statistical convergence of order α of cluster points and the set of Wijsman rough λ statistical convergence of order α limit points of a triple sequences of functions.

Analysis on the related factors of China's technological innovation ability using greyness relational degree

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Li Li ◽  
Xican Li
Keyword(s):  
Real Number ◽  
Technological Innovation ◽  
Number Sequence ◽  
Related Factors ◽  
Content Type ◽  
Grey Relational Degree ◽  
Relational Degree ◽  
Innovation Ability ◽  
Grey Number ◽  
Grey Relational

PurposeIn order to make grey relational analysis applicable to the interval grey number, this paper discusses the model of grey relational degree of the interval grey number and uses it to analyze the related factors of China's technological innovation ability.Design/methodology/approachFirst, this paper gives the definitions of the lower bound domain, the value domain, the upper bound domain of interval grey number and the generalized measure and the generalized greyness of interval grey number. Then, based on the grey relational theory, this paper proposes the model of greyness relational degree of the interval grey number and analyzes its relationship with the classical grey relational degree. Finally, the model of greyness relational degree is applied to analyze the related factors of China's technological innovation ability.FindingsThe results show that the model of greyness relational degree has strict theoretical basis, convenient calculation and easy programming and can be applied to the grey number sequence, real number sequence and grey number and real number coexisting sequence. The relational order of the four related factors of China's technological innovation ability is research and development (R&D) expenditure, R&D personnel, university student number and public library number, and it is in line with the reality.Practical implicationsThe results show that the sequence values of greyness relational degree have large discreteness, and it is feasible and effective to analyze the related factors of China's technological innovation ability.Originality/valueThe paper succeeds in realizing both the model of greyness relational degree of interval grey number with unvalued information distribution and the order of related factors of China's technological innovation ability.

Sign in / Sign up

Export Citation Format

Share Document