scholarly journals Statistical Cluster Points and Turnpike Theorem in Nonconvex Problems

2001 ◽  
Vol 256 (2) ◽  
pp. 686-693 ◽  
Author(s):  
Musa A. Mamedov ◽  
Serpil Pehlivan
Keyword(s):  
Nonconvex Problems ◽  
Statistical Cluster ◽  
Turnpike Theorem ◽  
Cluster Points

scholarly journals A-Statistical Cluster Points in Finite Dimensional Spaces and Application to Turnpike Theorem

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Pratulananda Das ◽  
Sudipta Dutta ◽  
S. A. Mohiuddine ◽  
Abdullah Alotaibi
Keyword(s):  
Optimal Control ◽  
Discrete Time ◽  
General Notion ◽  
Optimal Controls ◽  
General Version ◽  
Finite Dimensional ◽  
Optimal Paths ◽  
Statistical Cluster ◽  
Turnpike Theorem ◽  
Cluster Points

In the first part of the paper, following the works of Pehlivan et al. (2004), we study the set of allA-statistical cluster points of sequences inm-dimensional spaces and make certain investigations on the set of allA-statistical cluster points of sequences inm-dimensional spaces. In the second part of the paper, we apply this notion to study an asymptotic behaviour of optimal paths and optimal controls in the problem of optimal control in discrete time and prove a general version of turnpike theorem in line of the work of Mamedov and Pehlivan (2000). However, all results of this section are presented in terms of a more general notion ofℐ-cluster points.

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.

Statistical cluster points and turnpike*

Optimization ◽  
2000 ◽  
Vol 48 (1) ◽  
pp. 91-106 ◽  
Author(s):  
Serpil Pehlivan ◽  
Musa A Mamedov
Keyword(s):  
Statistical Cluster ◽  
Cluster Points

scholarly journals Statistical Cluster Points of Sequences in Finite Dimensional Spaces

2004 ◽  
Vol 54 (1) ◽  
pp. 95-102 ◽  
Author(s):  
S. Pehlivan ◽  
A. Güncan ◽  
M. A. Mamedov
Keyword(s):  
Finite Dimensional ◽  
Statistical Cluster ◽  
Cluster Points

scholarly journals On Cluster Points, Continuity, and Boundedness Associated with the Generalized Statistical Convergence in Probabilistic Normed Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Pratulananda Das ◽  
Kaustubh Dutta ◽  
Vatan Karakaya
Keyword(s):  
Statistical Convergence ◽  
Normed Spaces ◽  
Statistical Cluster ◽  
Probabilistic Normed Spaces ◽  
Extremal Limit ◽  
Limit Points ◽  
Appl Math ◽  
Cluster Points

We consider the recently introduced notion ofℐ-statistical convergence (Das, Savas and Ghosal, Appl. Math. Lett., 24(9) (2011), 1509–1514, Savas and Das, Appl. Math. Lett. 24(6) (2011), 826–830) in probabilistic normed spaces and in the following (Şençimen and Pehlivan (2008 vol. 26, 2008 vol. 87, 2009)) we introduce the notions like strongℐ-statistical cluster points and extremal limit points, and strongℐ-statistical continuity and strongℐ-statisticalD-boundedness in probabilistic normed spaces and study some of their important properties.

scholarly journals Deferred Statistical Cluster Points of Real Valued Sequences

2013 ◽  
Vol 1 (1) ◽  
pp. 1-6
Author(s):  
Mujde Yilmazturk ◽  
Ozgur Mizrak ◽  
Mehmet Kucukaslam
Keyword(s):  
Statistical Cluster ◽  
Cluster Points

When deviation happens between rough statistical convergence and rough weighted statistical convergence

2019 ◽  
Vol 69 (4) ◽  
pp. 871-890 ◽  
Author(s):  
Sanjoy Ghosal ◽  
Avishek Ghosh
Keyword(s):  
Statistical Convergence ◽  
Limit Set ◽  
Double Sequences ◽  
Statistical Cluster ◽  
Statistical Limit ◽  
Cluster Points

Abstract In this paper we introduce rough weighted statistical limit set and weighted statistical cluster points set which are natural generalizations of rough statistical limit set and statistical cluster points set of double sequences respectively. Some new examples are constructed to ensure the deviation of basic results. Both the sets don’t follow the usual extension properties which will be discussed here.

scholarly journals Effects on rough I-lacunary statistical convergence to induce the weighted sequence

Filomat ◽  
2018 ◽  
Vol 32 (10) ◽  
pp. 3557-3568 ◽  
Author(s):  
Sanjoy Ghosal ◽  
Mandobi Banerjee
Keyword(s):  
Statistical Convergence ◽  
Limit Set ◽  
Topological Approach ◽  
Weighted Sequence ◽  
Statistical Cluster ◽  
Statistical Limit ◽  
Lacunary Statistical Convergence ◽  
Cluster Points

Two classes of sets are introduced: rough weighted I-lacunary statistical limit set and weighted I-lacunary statistical cluster points set which are natural generalizations of rough I-limit set and I-cluster points set respectively. To highlight the variation from basic results we place into some new examples. So our aim is to analyze the different behaviors of the new convergences and characterize both the sets with topological approach like closedness, boundedness, compactness etc.

scholarly journals New Results on I 2 -Statistically Limit Points and I 2 -Statistically Cluster Points of Sequences of Fuzzy Numbers

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Ö. Kişi ◽  
M. B. Huban ◽  
M. Gürdal
Keyword(s):  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Double Sequence ◽  
Statistical Cluster ◽  
Statistical Limit ◽  
Number Sequences ◽  
Sequences Of Fuzzy Numbers ◽  
Limit Points ◽  
The Relationship ◽  
Cluster Points

In this paper, some existing theories on convergence of fuzzy number sequences are extended to I 2 -statistical convergence of fuzzy number sequence. Also, we broaden the notions of I -statistical limit points and I -statistical cluster points of a sequence of fuzzy numbers to I 2 -statistical limit points and I 2 -statistical cluster points of a double sequence of fuzzy numbers. Also, the researchers focus on important fundamental features of the set of all I 2 -statistical cluster points and the set of all I 2 -statistical limit points of a double sequence of fuzzy numbers and examine the relationship between them.

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