Browse > Article
http://dx.doi.org/10.22771/nfaa.2022.27.03.10

MEAN CONVERGENCE THEOREMS FOR DOUBLE ARRAY OF FUZZY RANDOM VARIABLES IN METRIC SPACES  

Nguyen, Pham Tri (Department of Mathematics, Electric Power University)
Publication Information
Nonlinear Functional Analysis and Applications / v.27, no.3, 2022 , pp. 621-640 More about this Journal
Abstract
The aim of this study is to establish some mean convergence theorems for double array of fuzzy random variables in metric space endowed with a convex combination operation under various assumptions.
Keywords
Convex combination space; fuzzy random variable; mean convergence theorem; compactly uniformly r-th order integrable in Cesaro sense (Cesaro r-th CUI);
Citations & Related Records
연도 인용수 순위
  • Reference
1 S. Li and Y. Ogura, Strong laws of large number for independent fuzzy set-valued random variables, Fuzzy Sets and Syst., 157 (2006), 2569-2578.   DOI
2 M.O. Cabrera and A. Volodin, Mean convergence theorems and weak laws of large numbers for weighted sums of random variables under a condition of weighted integrability, J. Math. Anal. Appl., 305 (2005), 644-658.   DOI
3 P. Teran and I. Molchanov, The law of large numbers in a metric space with a convex combination operation, J. Theoretical Prob., 19 (2006), 875-898.   DOI
4 A. Adler, A. Rosalsky and A. Volodin, A mean convergence theorem and weak law for arrays of random elements in martingale type p Banach spaces, Statist. Probab. Lett., 32 (1997), 167-174.   DOI
5 K.A. Fu and L.X. Zhang, Strong laws of large numbers for arrays of rowwise independent random compact sets and fuzzy random sets, Fuzzy Sets and Syst., 159 (2008), 3360-3368.   DOI
6 S.I.E. Manna and A.A. Eldred, Weak and Strong Convergence Theorems for Three Step Iteration of Asymptotically Firmly Type Nonexpansive Mappings, Nonlinear Funct. Anal. Appl., 24(4) (2019), 747-757.
7 N.V. Quang and P.T. Nguyen, Some strong laws of large number for double array of random upper semicontinuous functions in convex combination spaces, Statist. Probab. Lett., 96 (2015), 85-94.   DOI
8 P. Teran and I. Molchanov, A general law of large numbers with applications, Advan. Soft Comput., 6 (2006), 153-160.
9 P. Bai, P.Y. Chen and S.H. Sung, On complete convergence and the strong law of large numbers for pairwise independent random variables, Acta Math. Hungar., 142 (2014), 502-518.   DOI
10 L.V. Thanh, Strong law of large numbers and Lp-convergence for double arrays of independent random variables, Acta Math. Viet., 30(3) (2005), 225-232.
11 N.T. Thuan, Approach for a metric space with a convex combination operation and applications, J. Math. Anal. Appl., 435(1) (2016), 440-460.   DOI
12 N.T. Thuan and N.V. Quang, Baum-Katz type theorems for pairwise independent random elements in certain metric spaces, Acta Math. Viet., 45 (2020), 555-570.   DOI
13 N.T. Thuan, N.V. Quang and P.T. Nguyen, Complete convergence for arrays of rowwise independent random variables and fuzzy random variables in convex combination spaces, Fuzzy Sets and Syst., 250 (2014), 52-68.   DOI
14 Y. Wu and M. Guan, Mean convergence theorems and weak laws of large numbers for weighted sums of dependent random variables, J. Math. Anal. Appl., 377 (2011), 613-623.   DOI
15 P. Chen and D. Wang, Lr convergence for B-valued random elements, Acta Math. Sinica, English Series, 28 (2012), 857-868.   DOI
16 X. Hua and G. Fang, Strong laws of large numbers and mean convergence theorems for randomly weighted sums of arrays under a condition of integrability, Statistical Methodology, 9 (2012), 528-536.   DOI
17 G.A. Okeke, J.O. Olaleru and J.K. Kim, Mean convergence theorems for asymptotically demicontractive mappings in the intermediate sense, Nonlinear Funct. Anal. Appl., 23(4) (2018), 613-627.
18 M.L. Puri and D.A. Ralescu, Fuzzy random variables, J. Math Anal. Appl., 114(2) (1986), 409-422.   DOI
19 N.V. Quang and N.T. Thuan, On the strong laws of large number for double arrays of random variables in convex combination spaces, Acta Math. Hungar, 134 (2012), 543-564.   DOI
20 D. Yuan and B. Tao, Mean convergence theorems for weighted sums of arrays of residually h-integrable random variables concerning the weights under dependence assumptions, Acta Appl. Math., 103 (2008), 221-234.   DOI
21 S.H. Sung, Convergence in r-mean of weighted sums of NQD random variables, Appl. Math. Lett., 26 (2013), 18-24.   DOI