• Korean Journal of Mathematics
• /
• 제21권4호
• /
• pp.375-382
• /
• 2013

In this paper, I introduce the notion of regular convergence space and give some properties of this space. And I give some conditions for the regularity of continuous convergence structure.

• 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.

• East Asian mathematical journal
• /
• 제26권3호
• /
• pp.365-370
• /
• 2010

A local convergence result is provided for the continuous analog of Newton's method in a Banach space setting. The radius of convergence is larger, the error bounds tighter, and under the same or weaker hypotheses than before [12].

• 한국수학교육학회지시리즈D:수학교육연구
• /
• 제17권2호
• /
• pp.133-152
• /
• 2013

In this research, we investigated students' understanding of the definitions of sequence of continuous functions and its uniform convergence. We selected three female and three male students out of the senior class of a university and conducted questionnaire surveys 4 times. We examined students' concept images of sequence of continuous functions and its uniform convergence and also how they approach to the right concept definitions for those through several progressive questions. Furthermore, we presented some suggestions for effective teaching-learning for the sequences of continuous functions.

• 호남수학학술지
• /
• 제33권2호
• /
• pp.279-300
• /
• 2011

For a subset system M on any poset, M-Scott notions, such as M-way below relation,M-continuity,M-Scott convergence (of nets and filters respectively) and M-Scott topology are proposed Any approximating auxiliary relation on a poset can be represented by an M-way below relation such that this poset is M-continuous. It is shown that a poset is M-continuous iff the M-Scott topology is completely distributive. The topology induced by the M-Scott convergence coincides with the M-Scott topology. If the M-way below relation satisfies the property of interpolation then a poset is M-continuous if and only if the M-Scott convergence coincides with the M-Scott topological convergence. Also, M-continuity is characterized by a certain Galois connection.

• East Asian mathematical journal
• /
• 제25권2호
• /
• pp.153-157
• /
• 2009

Motivated by optimization considerations we revisit the work by Dontchev in [7] involving the convergence of Newton's method to a solution of a generalized equation in a Banach space setting. Using the same hypotheses and under the same computational cost we provide a finer convergence analysis for Newton's method by using more precise estimates.

• 한국산업융합학회 논문집
• /
• 제17권3호
• /
• pp.122-135
• /
• 2014

This paper was studied on the horizontal continuous casting of Al-xSi(x=10~15%) aluminum alloy. The experiments of the horizontal continuous casting was carried out by the horizontal continuous casting machine for various casting conditions and investigated on fracture types and mechanisms. Surface defect types for the horizontal continuous casting is also investigated. And the study was carried out that the horizontal continuous casting conditions such as casting temperature, cooling rate, and drawing speed affect the hardness and primary silicon size of Al-xSi(x=10~15%) aluminum rod bar. Casting temperature within this experiment conditions don't affect on the hardness of rod bar but the higher casting temperature is the smaller primary silicon size. The higher cooling rate and drawing speed have the higher hardness and the smaller primary silicon size.

• 대한수학회지
• /
• 제54권1호
• /
• pp.319-357
• /
• 2017

There are presented certain results on extending continuous linear operators defined on spaces of E-valued continuous functions (defined on a compact Hausdorff space X) to linear operators defined on spaces of E-valued measurable functions in a way such that uniformly bounded sequences of functions that converge pointwise in the weak (or norm) topology of E are sent to sequences that converge in the weak, norm or weak* topology of the target space. As an application, a new description of uniform closures of convex subsets of C(X, E) is given. Also new and strong results on integral representations of continuous linear operators defined on C(X, E) are presented. A new classes of vector measures are introduced and various bounded convergence theorems for them are proved.

• 호남수학학술지
• /
• 제36권3호
• /
• pp.669-678
• /
• 2014

We investigate various properties of ${\kappa}$-net convergence structures and define a ${\kappa}$-net-based continuous function on ${\kappa}$-net $\mathcal{L}^+$-convergence structures, and study relationships between continuity and ${\kappa}$-net-based continuity on ${\kappa}$-net $\mathcal{L}^+$-convergence structures. We also provide some characterizations of ${\kappa}$-net-based continuity.

• East Asian mathematical journal
• /
• 제28권3호
• /
• pp.287-292
• /
• 2012

In this paper, we establish the strong convergence for the Mann iterative scheme associated with uniformly continuous pseudocontractive mappings in real Banach spaces. Moreover, our technique of proofs is of independent interest.