• Korean Journal of Mathematics
• /
• 제27권4호
• /
• pp.861-877
• /
• 2019

The aim of this paper is to extend some existing fixed point results for asymptotically regular mappings to fuzzy metric spaces. For this purpose some contractive type conditions with respect to an altering distance function are used. Some new common fixed point results have been derived for such mappings. We provide suitable examples to justify our study.

• East Asian mathematical journal
• /
• 제14권2호
• /
• pp.343-356
• /
• 1998

In this paper, we prove some common fixed point theorems for compatible mappings by using asymptotically regular mappings under the contractive type of G. E. Hardy and T. D. Rogers, and also give some examples to illustrate our main theorems. Our results extend the results of M. D. Guay and K. L. Singh and others.

• 대한수학회논문집
• /
• 제13권3호
• /
• pp.501-513
• /
• 1998

In this paper, we deal with the asymptotic behavior for the almost-orbits {u(t)} of an asymptotically nonexpansive semigroup S = {S(t) : t $\in$ G} for a right reversible semitopological semigroup G, defined on a suitable subset C of Banach spaces with the Opial's condition, locally uniform Opial condition, or uniform Opial condition.

• 대한수학회논문집
• /
• 제12권2호
• /
• pp.237-250
• /
• 1997

In this paper, we study the asymptotic behavior of orbits ${S(t)x}$ of an asymptotically nonexpansive semigroup $S = {S(t) : t \in G}$ for a right reversible semitopological semigroup G, defined on a weakly compact convex subset C of Banach spaces with Opial's condition for any $x \in C$.

• Kyungpook Mathematical Journal
• /
• 제45권3호
• /
• pp.433-443
• /
• 2005

In 1994, Lim-Xu asked whether the Maluta's constant D(X) < 1 implies the fixed point property for asymptotically nonexpansive mappings and gave a partial solution for this question under an additional assumption for T, i.e., weakly asymptotic regularity of T. In this paper, we shall prove that the result due to Lim-Xu is also satisfied for more general non-Lipschitzian mappings in reflexive Banach spaces with weak uniform normal structure. Some applications of this result are also added.

• East Asian mathematical journal
• /
• 제8권2호
• /
• pp.171-183
• /
• 1992

• 대한수학회보
• /
• 제37권4호
• /
• pp.729-741
• /
• 2000

In this paper, we study in Banach spaces the existence of fixed points of asymptotically regular mapping T satisfying: for each x, y in the domain and for n=1, 2,…, $$\parallelT^nx-T^ny\parallel\leq$\leq$a_n\parallelx-y\parallel+b_n (\parallelx-T^nx\parallel+\parallely-T^ny\parallely)$$ where $a_n,\; b_n,\; C_n$ are nonnegative constants satisfying certain conditions. We also establish some fixed point theorems for these mappings in a Hibert space, in L(sup)p spaces, in Hardy space H(sup)p, and in Soboleve space $H^{k,p} for 1<\rho<\infty \; and \; k\geq0$. We extend results from papers [10], [11], and others.

• Journal of the Korean Statistical Society
• /
• 제26권3호
• /
• pp.383-395
• /
• 1997

This paper proves that the standard bootstrap approximation for the least absolute deviation (LAD) estimate of .beta. in AR(1) processes with infinite variance error terms is asymptotically valid in probability when the bootstrap resample size is much smaller than the original sample size. The theoretical validity results are supported by simulation studies.

• 대한수학회지
• /
• 제45권5호
• /
• pp.1393-1404
• /
• 2008

Let K be a nonempty closed convex subset of a Banach space E. Suppose $\{T_{n}\}$ (n = 1,2,...) is a uniformly asymptotically regular sequence of nonexpansive mappings from K to K such that ${\cap}_{n=1}^{\infty}$ F$\(T_n){\neq}{\phi}$. For $x_0{\in}K$, define $x_{n+1}={\lambda}_{n+1}x_{n}+(1-{\lambda}_{n+1})T_{n+1}x_{n},n{\geq}0$. If ${\lambda}_n{\subset}[0,1]$ satisfies $lim_{n{\rightarrow}{\infty}}{\lambda}_n=0$, we proved that $\{x_n\}$ weakly converges to some $z{\in}F\;as\;n{\rightarrow}{\infty}$ in the framework of reflexive Banach space E which satisfies the Opial's condition or has $Fr{\acute{e}}chet$ differentiable norm or its dual $E^*$ has the Kadec-Klee property. We also obtain that $\{x_n\}$ strongly converges to some $z{\in}F$ in Banach space E if K is a compact subset of E or there exists one map $T{\in}\{T_{n};n=1,2,...\}$ satisfy some compact conditions such as T is semi compact or satisfy Condition A or $lim_{n{\rightarrow}{\infty}}d(x_{n},F(T))=0$ and so on.

• 대한수학회논문집
• /
• 제11권3호
• /
• pp.725-742
• /
• 1996

In this paper we give some sharp expressions of the weakly convergent sequence coefficient WCS(X) of a Banach space X. They are used to prove fixed point theorems for involution mappings T from a weakly compact convex subset C of a Banach space X with WCS(X) > 1 into itself which $T^2$ are both of asymptotically nonexpansive type and weakly asymptotically regular on C. We also show that if X satisfies the semi-Opial property, then every nonexpansive mapping $T : C \to C$ has a fixed point. Further, some questions for asymtotically nonexpansive mappings are raised.