Báo cáo hóa học: " Some strong limit theorems for arrays of rowwise negatively orthant-dependent random variables Aiting Shen" pptx

... the strong limit theorems for arrays of rowwise negatively orthant- dependent random variables are studied. Some sufficient conditions for stro ng law of large numbers for an array of rowwise negatively ... is to study the strong limit theorems for arrays of rowwise NOD random variables. As an application, the Chung-type strong law of lar...

Ngày tải lên: 20/06/2014, 22:20

... w n )=0.Thismeansthat{w n }con- verges to v 0 , and the proof is completed. □ For a metric space (X, d), we will denote by Cl(X) the set of all closed subsets of X. In view of proving Lemma 2.3, we can obtain a fixed ... α n )+ 1 n , (2:3) for all n Î N. Using such a function f, we now define a function g: N ® N by g(n)=  1, if n < f (1), k,iff (k) ≤ n < f (k +1) forsomek ∈ ....

Ngày tải lên: 20/06/2014, 22:20

... new common fixed point theorems for weakly com- patible mappings on uniform spaces. While, Nashine and Samet [12] proved some new coincidence point theorems for a pair of weakly increasing mappings. ... proved some coincidence point theorems for a pair of weakly increasing mappings with respect to another map. The aim of this article is to study new coincidence point the...

Ngày tải lên: 20/06/2014, 22:20

... 13 [40] proved some more generalizations of coupled fixed point theorems in partially ordered sets. Recently, Gordji et al. [41] proved some coupled coincidence point theorems for con- tractive ... improve and extend some couple fixed point theorems due to Gordji et al. [41] and other couple fixed point theorems. 2. Preliminaries Now, we give some definitions, examples and...

Ngày tải lên: 20/06/2014, 22:20

... |O|   ρ 2 O |v| q dμ  1 q . (3:4) Therefore, we have completed the proof of Theorem 2.6. By Lemma 2.5 and Theorem 2.6, we obtain the proof of Theorem 2.4. ProofofTheorem2.4.First,weobservethat μ(O)=  O ν(x)dx ... independent of ν, such that   O |T(d(H(v))) − (T(d(H(v)))) O | q dμ  1 q ≤ Cdia m( O) |O|   ρ O |v| q dμ  1 q (2:8) for all balls O with rO ⊂ Θ for some r >1...

Ngày tải lên: 20/06/2014, 22:20

... ||Tx n || ) for all n Î N, we get lim m →∞ (x n − Tx n )= 0 .AsT is semicompact, there exist a subse- quence {x m }of{ x n }inM such that lim m →∞ x m = y for some y Î M. By definition of T m , we ... Research Professional Development Project Under the Science Achievement Scholarship of Thailand (SAST) and the Faculty of Science, KMUTT for finan cial support during the preparat...

Ngày tải lên: 20/06/2014, 22:20

... (or B ≤ * D). Proof. The proof is trivial and therefore omitted. Since A ∗ ≤ B and A ≤ * B are equivalent to A ∗ ∗ ≤ B ∗ and A ∗ ∗ ≤ B ∗ , respectively, there- fore, for the rowwise partitioned ... then A + B ∗ ≤ C + D . Proof. The proof is trivial and therefore omitted. □ 3 Minus partial ordering In this section, we present some results on the minus orderings of the matrix product an...

Ngày tải lên: 21/06/2014, 00:20

... and {λ n }⊂(0, α K 2 ] . For convenience, we write y n ≡ Q C ( x n - l n Ax n ). 3.1. Some properties of the sequence {x n } for weak convergence theorems We star t with some propositions, which ... convergence of the sequence of successive approximations for nonexpansive mappings. Bull Am Math Soc. 73, 591–597 (1967). doi:10.1090/S0002-9904-1967-11761-0 9. Reich, S: Weak co...

Ngày tải lên: 21/06/2014, 01:20

... theorem of partial sums of random variables and obtained lots of classical results for sequences of independent random variables and martingale differences. For a detailed survey of strong limit theorems ... class of strong limit theorems for arbitrary stochastic sequence. Chow’s two strong limit theorems for martingale- difference sequence and Lo `...

Ngày tải lên: 21/06/2014, 07:20

... properties of E with the help of E C . Without loss of generality, we can deal only with the positive solutions of E. Since every solution of E is also a solution of E C , we are in view of ... techniques appeared for the investigation of such equations. Some of them 1, 19 make use of the methods developed for the second-order equations 16, 17, 20 like...

Ngày tải lên: 21/06/2014, 11:20