• Journal of applied mathematics & informatics
• /
• v.28 no.3_4
• /
• pp.993-1001
• /
• 2010

In this paper, we introduce the concept of fuzzy weakly r-M continuous function on r-minimal structures and investigate characterizations and properties for such functions.

• Communications of the Korean Mathematical Society
• /
• v.17 no.4
• /
• pp.675-680
• /
• 2002

Since N. Levin [1] in 1961 defined the weakly continuous function, there is a lot of weakened forms of continuous function. In this paper we consider two forms of the weakened form of continuous function and study the some properties of them.

• Journal of Korean Society of Industrial and Systems Engineering
• /
• v.36 no.2
• /
• pp.8-16
• /
• 2013

In this paper, we proposed a new method for the determination of strategies that are required in a continuous optimization algorithm based on the fictitious play theory. In order to apply the fictitious play theory to continuous optimization problems, it is necessary to express continuous values of a variable in terms of discrete strategies. In this paper, we proposed a method in which all strategies contain an equal number of selected real values that are sorted in their magnitudes. For comparative analysis of the characteristics and performance of the proposed method of representing strategies with respect to the conventional method, we applied the method to the two types of benchmarking functions: separable and inseparable functions. From the experimental results, we can infer that, in the case of the separable functions, the proposed method not only outperforms but is more stable. In the case of inseparable functions, on the contrary, the performance of the optimization depends on the benchmarking functions. In particular, there is a rather strong correlation between the performance and stability regardless of the benchmarking functions.

• Journal of applied mathematics & informatics
• /
• v.26 no.1_2
• /
• pp.75-106
• /
• 2008

In this paper, we derive necessary optimality conditions for a continuous programming problem in which both objective and constraint functions contain support functions and is, therefore, nondifferentiable. It is shown that under generalized invexity of functionals, Karush-Kuhn-Tucker type optimality conditions for the continuous programming problem are also sufficient. Using these optimality conditions, we construct dual problems of both Wolfe and Mond-Weir types and validate appropriate duality theorems under invexity and generalized invexity. A mixed type dual is also proposed and duality results are validated under generalized invexity. A special case which often occurs in mathematical programming is that in which the support function is the square root of a positive semidefinite quadratic form. Further, it is also pointed out that our results can be considered as dynamic generalizations of those of (static) nonlinear programming with support functions recently incorporated in the literature.

• East Asian mathematical journal
• /
• v.17 no.1
• /
• pp.1-17
• /
• 2001

In this paper, fuzzy D-continuous function is defined. Some basic properties of this continuity are summarized; and sufficient conditions on domain and/or ranges implying fuzzy D-continuity of fuzzy D-continuous functions are given. Also fuzzy D-regular space is defined and by using fuzzy D-continuity, the condition which is equivalent to fuzzy D-regular space, is given.

• The Pure and Applied Mathematics
• /
• v.23 no.1
• /
• pp.21-34
• /
• 2016

In this paper, we construct a strictly increasing continuous singular function which has a simple algebraic expression.

• The Pure and Applied Mathematics
• /
• v.17 no.2
• /
• pp.145-150
• /
• 2010

In this paper, we introduce the concepts of faintly ${\gamma}$-continuity and extremely ${\gamma}$-closed graph. And we study characterizations of such functions and relationships between faintly ${\gamma}$-continuity and extremely ${\gamma}$-closed graph.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.10 no.2
• /
• pp.124-127
• /
• 2010

In this paper, we introduce the concepts of fuzzy r-minimal continuous function and fuzzy r-minimal open function between a fuzzy r-minimal space and a fuzzy topological space. We also investigate characterizations and properties for such functions.

• Communications of the Korean Mathematical Society
• /
• v.11 no.1
• /
• pp.169-174
• /
• 1996

Let $C_\alpha$ be the collection of those members of $C[0,1]$ which are H$\ddot{o}lder $\alpha$-continuous functions on [0,1]. In this paper, I will show that $\mu(C_{\frac{1}{2}) = 0$ for Wiener measure $\mu$.

• Bulletin of the Korean Mathematical Society
• /
• v.51 no.2
• /
• pp.437-442
• /
• 2014

In this paper we prove Ekeland's variational principle in the setting of locally complete spaces for lower semi continuous functions from above and bounded below. We use this theorem to prove Caristi's fixed point theorem in the same setting and also for lower semi continuous functions.