A convergence structure generalizing the order convergence structure on the set of Hausdorff continuous interval functions is defined on the set of minimal usco maps. The properties of the obtained convergence space are investigated and essential links with the pointwise convergence and the order convergence are revealed. The convergence structure can be extended to a uniform convergence struct...

and Applied Analysis 3 2. Preliminaries In this section, wewill present some important lemmaswhich will be used to prove the main results of the paper. The first three lemmas come from Sung [1]. Lemma 11 (cf.[1]). Let {a n , n ≥ 1} be a sequence of positive constants with a n /n ↑. Then the following properties hold. (i) {a n , n ≥ 1} is a strictly increasing sequence with an a n ↑ ∞. (ii) ∑∞ n...

The authors first present a Rosenthal inequality for sequence of extended negatively dependent (END) random variables. By means of the Rosenthal inequality, the authors obtain some complete moment convergence and mean convergence results for arrays of rowwise END random variables. The results in this paper extend and improve the corresponding theorems by Hu and Taylor (1997).

Recently we proposed a new type of fuzzy integrals defined over complete residuated lattices. These integrals are intended for the modeling of type ⟨1, 1⟩ fuzzy quantifiers. An interesting theoretical question is, how to introduce various notions of convergence of this type of fuzzy integrals. In this contribution, we would like to present some results on strong and pointwise convergence of the...

Experimental results show that certain message passing algorithms, namely, Survey Propagation, are very effective in finding satisfying assignments for random satisfiable 3CNF formulas which are considered hard for other SAT heuristics. Unfortunately, rigorous understanding of this phenomena is still lacking. In this paper we make a modest step towards providing rigorous explanation for the eff...

Abstract. Let {Xn,n≥1} be a sequence of negatively superadditive dependent (NSD, in short) random variables and {ank,1≤ k≤n,n≥1} be an array of real numbers. Under some suitable conditions, we present some results on complete convergence for weighted sums ∑k=1ankXk of NSD random variables by using the Rosenthal type inequality. The results obtained in the paper generalize some corresponding one...

This paper establishes two results for complete convergence in the law of large numbers for arrays under %-mixing and ~ %-mixing association in rows. They extend several known results. AMS classi cation: 60F15

For arrays of independent Pareto random variables, this paper establishes complete convergence for weighted partial sums for the smaller order statistics within each row. This result improves on past strong laws. Moreover, it shows that we can obtain a finite nonzero limit for our normalized partial sums under complete convergence even though the first moment of our order statistics is infinite.

* Correspondence: volodin@math. uregina.ca Department of Mathematics and Statistics, University of Regina, Regina Saskatchewan S4S 0A2, Canada Full list of author information is available at the end of the article Abstract Some exponential inequalities for a sequence of acceptable random variables are obtained, such as Bernstein-type inequality, Hoeffding-type inequality. The Bernsteintype ineq...