• Journal of the Chungcheong Mathematical Society
• /
• v.33 no.1
• /
• pp.133-146
• /
• 2020

In this paper, we established the complete moment convergence for sequences of m-pairwise negatively quadrant dependent random variables which are weakly upper bounded by a random variable X.

• The Pure and Applied Mathematics
• /
• v.2 no.1
• /
• pp.1-8
• /
• 1995

Since the concept of Pettis integral was introduced in 1938 [10], the Pettis integrability of weakly measurable functions has been studied by many authors [5, 6, 7, 8, 9, 11]. It is known that there is a bounded function that is not Pettis integrable [10, Example 10. 8]. So it is natural to raise the question: when is a bounded function Pettis integrable\ulcorner(omitted)

• Journal of the Korean Institute of Intelligent Systems
• /
• v.6 no.3
• /
• pp.89-93
• /
• 1996

In this paper, we investigated the relation between the ideals of BCK-algebras and fuzzy ideals. We defined the weakly implicative ideals of BCK-algebras and obtained some properties. We proved some results for the fuzzy weakly implicative ideals of bounded commutative BCK-algebras. We also investigated that the weakly implicative ideals are similar to the fuzzy positive implicative ideals.

• Bulletin of the Korean Mathematical Society
• /
• v.42 no.2
• /
• pp.359-367
• /
• 2005

Let A be a Banach algebra, we say that A has the strongly double limit property (SDLP) if for each bounded net $(a_\alpha)$ in A and each bounded net $(a^{\ast}\;_\beta)\;in\;A^{\ast},\;lim_\alpha\;lim_\beta=lim_\beta\;lim_\alpha$ whenever both iterated limits exist. In this paper among other results we show that if A has the SDLP and $A^{\ast\ast}$ is (n - 2)-weakly amenable, then A is n-weakly amenable. In particular, it is shown that if $A^{\ast\ast}$ is weakly amenable and A has the SDLP, then A is weakly amenable.

• The Pure and Applied Mathematics
• /
• v.4 no.1
• /
• pp.87-92
• /
• 1997

Some function of a complete finite measure space (for short, CFMS) into the duals and pre-duals of weakly compactly generated (for short, WCG) spaces are considered. We shall show that a universally weakly measurable function f of a CFMS into the dual of a WCG space has RS property and bounded weakly measurable functions of a CFMS into the pre-duals of WCG spaces are always Pettis integrable.

• The Pure and Applied Mathematics
• /
• v.1 no.1
• /
• pp.25-27
• /
• 1994

Suppose that X is a Banach space with continuous dual $X^{**}$, ($\Omega$, $\Sigma$, ${\mu}$) is a finite measure space. f : $\Omega\;{\longrightarrow}$ $X^{*}$ is a weakly measurable function such that $\chi$$^{**}$ f $\in$ $L_1$(${\mu}$) for each $\chi$$^{**}$ $\in$ $X^{**}$ and $T_{f}$ : $X^{**}$ \longrightarrow $L_1$(${\mu}$) is the operator defined by $T_{f}$($\chi$$^{**}$) = $\chi$$^{**}$f. In this paper we study the properties of bounded $X^{*}$ - valued weakly measurable functions and bounded $X^{*}$ - valued weak＊ measurable functions.(omitted)

• East Asian mathematical journal
• /
• v.24 no.2
• /
• pp.201-212
• /
• 2008

We characterize operators between Banach spaces sending unconditionally weakly p-summable sequences into sequences that lie in the range of a vector measure of bounded variation. Further, we describe operators between Banach spaces taking unconditionally weakly p-summable sequences into sequences that lie in the range of a vector measure.

• The Pure and Applied Mathematics
• /
• v.28 no.1
• /
• pp.1-13
• /
• 2021

In this note we use a generalization of coincidence point(a property which was defined by [1] in symmetric spaces) to prove common fixed point theorem on S-metric spaces for weakly compatible maps. Also the results are used to achieve the solution of an integral equation and the bounded solution of a functional equation in dynamic programming.

• Bulletin of the Korean Mathematical Society
• /
• v.37 no.2
• /
• pp.209-215
• /
• 2000

Let X be a locally convex space. A series of clearcut characterizations for the boundedness of vector measure $\mu{\;}:{\;}\sum\rightarrow{\;}X$ is obtained, e.g., ${\mu}$ is bounded if and only if ${\mu}(A_j){\;}\rightarrow{\;}0$ weakly for every disjoint $\{A_j\}{\;}\subseteq{\;}\sum$ and if and only if $\{\frac{1}{j^j}{\mu}(A_j)\}^{\infty}_{j=1}$ is bounded for every disjoint $\{A_j\}{\;}\subseteq{\;}\sum$.

• Korean Journal of Mathematics
• /
• v.5 no.2
• /
• pp.195-198
• /
• 1997

In this paper, we have some characterizations of Pettis integrability of bounded weakly measurable function $f:{\Omega}{\rightarrow}X^*$ determined by separable subspace of $X^*$.