• Journal of the Korean Statistical Society
• /
• 제24권2호
• /
• pp.273-280
• /
• 1995

This paper gives a generalization of an $L_1$-convergence theorem for dependent processes due to Andrews (1988) and also a probability convergence theorem.

• 대한수학회논문집
• /
• 제11권3호
• /
• pp.855-865
• /
• 1996

In this paper, we establish the weak convergences of processes occurring in a generalized Curie-Weiss model and its dual.

• Journal of applied mathematics & informatics
• /
• 제26권1_2호
• /
• pp.325-336
• /
• 2008

In this paper, we prove the weak and strong convergence of the three-step iterative scheme with errors to a common fixed point for two asymptotically nonexpansive mappings in a uniformly convex Banach space under a condition weaker than compactness. Our theorems improve and generalize some previous results.

• Journal of the Korean Statistical Society
• /
• 제32권2호
• /
• pp.203-211
• /
• 2003

A new result of weak convergence of the empirical process is established for a stationary ${\phi}-mixing$ sequence of random variables, which relaxes the existing conditions on mixing coefficients. The result is basically obtained from bounds for even moments of sums of ${\phi}-mixing$ r.v.'s useful for handling triangular arrays with entries decreasing in size.

• Communications for Statistical Applications and Methods
• /
• 제15권6호
• /
• pp.959-967
• /
• 2008

In this paper we show the weak convergence of the linear random(multistochastic process) field generated by identically distributed 2-parameter array of associated random variables. Our result extends the result in Newman and Wright (1982) to the linear 2-parameter processes as well as the result in Kim and Ko (2003) to the 2-parameter case.

• 대한수학회지
• /
• 제52권6호
• /
• pp.1179-1194
• /
• 2015

In this paper, we introduce a new iterative algorithm for finding a common element of the set of solutions of a generalized mixed equilibrium problem related to a continuous monotone mapping, the set of solutions of a variational inequality problem for a continuous monotone mapping, and the set of fixed points of a continuous pseudocontractive mapping in Hilbert spaces. Weak convergence for the proposed iterative algorithm is proved. Our results improve and extend some recent results in the literature.

• Journal of the Korean Statistical Society
• /
• 제31권1호
• /
• pp.109-120
• /
• 2002

In this paper, we show the weak convergence of U-empirical processes for two sample problem. We use the result to show the asymptotic normality for the generalized dodges-Lehmann estimates with the Bahadur representation for quantifies of U-empirical distributions. Also we consider the asymptotic normality for the test statistics in a simple way.

• Journal of applied mathematics & informatics
• /
• 제23권1_2호
• /
• pp.525-536
• /
• 2007

In this paper, we prove the weak and strong convergence of the Noor iterative scheme to a common fixed point for two asymptotically nonexpansive mappings in a uniformly convex Banach space under a condition weaker than compactness. Our theorems improve and generalize some previous results.

• 대한수학회논문집
• /
• 제25권4호
• /
• pp.583-607
• /
• 2010

The purpose of this paper is to prove strong convergence theorems for common fixed points of two families of weak relatively nonexpansive mappings and a family of equilibrium problems by a new monotone hybrid method in Banach spaces. Because the hybrid method presented in this paper is monotone, so that the method of the proof is different from the original one. We shall give an example which is weak relatively nonexpansive mapping but not relatively nonexpansive mapping in Banach space $l^2$. Our results improve and extend the corresponding results announced in [W. Takahashi and K. Zembayashi, Strong convergence theorem by a new hybrid method for equilibrium problems and relatively nonexpansive mappings, Fixed Point Theory Appl. (2008), Article ID 528476, 11 pages; doi:10.1155/2008/528476] and [Y. Su, Z. Wang, and H. Xu, Strong convergence theorems for a common fixed point of two hemi-relatively nonexpansive mappings, Nonlinear Anal. 71 (2009), no. 11, 5616?5628] and some other papers.

• 충청수학회지
• /
• 제28권1호
• /
• pp.1-12
• /
• 2015

We present a local convergence analysis for inexact Newton-like method in a Banach space under weaker Lipschitz condition. The convergence ball is enlarged and the estimates on the error distances are more precise under the same computational cost as in earlier studies such as [6, 7, 11, 18]. Some special cases are considered and applications for solving nonlinear systems using the Newton-arithmetic mean method are improved with the new convergence technique.