• Bulletin of the Korean Mathematical Society
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• v.48 no.5
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• pp.939-949
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• 2011

In this paper we give two matching theorems of Ky Fan type concerning open or closed coverings of nonempty convex sets in a topological vector space. One of them will permit us to put in evidence, when X and Y are convex sets in topological vector spaces, a new subclass of KKM(X, Y) different by any admissible class $\mathfrak{u}_c$(X, Y). For this class of set-valued mappings we establish a KKM-type theorem which will be then used for obtaining existence theorems for the solutions of two types of simultaneous relation problems.

• Communications of the Korean Mathematical Society
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• v.32 no.4
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• pp.933-957
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• 2017

In this paper, we prove some existence results of solutions for a new class of generalized bi-quasi-variational-like inequalities (GBQVLI) for (${\eta}-h$)-quasi-pseudo-monotone type I and strongly (${\eta}-h$)-quasi-pseudo-monotone type I operators defined on non-compact sets in locally convex Hausdorff topological vector spaces. To obtain our results on GBQVLI for (${\eta}-h$)-quasi-pseudo-monotone type I and strongly (${\eta}-h$)-quasi-pseudo-monotone type I operators, we use Chowdhury and Tan's generalized version of Ky Fan's minimax inequality as the main tool.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.10 no.3
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• pp.242-246
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• 2010

It is well-known that the space $E^n$ of fuzzy numbers(i.e., normal, upper-semicontinuous, compact-supported and convex fuzzy subsets)in the n-dimensional Euclidean space $R^n$ is separable but not complete with respect to the $L_p$-metric. In this paper, we introduce the space $F_p(R^n)$ that is separable and complete with respect to the $L_p$-metric. This will be accomplished by assuming p-th mean bounded condition instead of compact-supported condition and by removing convex condition.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.1
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• pp.166-174
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• 1994

A critical evaluation is made of the spectral bias which occurs in the use of a laser doppler velocimeter(LDV). Two processing algorithms are considered for spectral estimates: the sample and hold interpolation method(SH) and the nonuniform Shannon reconstruction technique(SR). Assessment is made of these for varying data densities $(0.05{\le}d.d.{\le}5)$ and turbulence levels(t.i.=30%, 100%). As an improved version of the spectral estimator, the utility of POCS (the projection onto convex sets) has been tested in the present study. This algorithm is found useful to be in the region when $d.d.{\gep}3.$

• Honam Mathematical Journal
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• v.27 no.1
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• pp.9-30
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• 2005

The notion of intuitionistic fuzzy convex sublattices is introduced, and its characterization is given. Natural equivalence relations on the set of all intuitionistic fuzzy ideals/filters of a lattice are investigated. Operations on intuitionistic fuzzy sets of a lattice is introduced. Some results of intuitionistic fuzzy ideals/filters under these operations are provided. Using these operations, characterizations of intuitionistic fuzzy ideals/filters are given.

• Korean Journal of Mathematics
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• v.27 no.2
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• pp.279-295
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• 2019

In this paper, using local fractional integrals on fractal sets $R^{\alpha}(0<{\alpha}{\leq}1)$ of real line numbers, we establish new some inequalities of Simpson's type based on generalized convexity.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.29 no.11C
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• pp.1592-1599
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• 2004

In this paper, we proposed the 3D mesh watermarking using projection onto convex sets (POCS). 3D mesh is projected iteratively onto two constraint convex sets until it satisfy the convergence condition. These sets consist of the robustness set and the invisibility set that designed to embed watermark Watermark is extracted without original mesh by using the decision values and the index that watermark is embedded. Experimental results verified that the watermarked mesh have the robustness against mesh simplification, cropping, affine transformation, and vertex randomization as well as the invisibility.

• 제어로봇시스템학회:학술대회논문집
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• 1997.10a
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• pp.1876-1879
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• 1997

This paper developes an efficient algorithm for the minimum distance calculation between general polyhedra(convex and/or concave). The polyhedron approximates and object using flat polygons which composed of more than three veritices. The algorithm developed in this paper basically computes minimun distance betwen two convex polygons and finds a set of polygons whcih makes a global minimum distance. The advantage of the algorithm is that the global minimum distance can be computed in any cases. But the big disadvantage is that minimum distance computing time is repidly increased with the number of polygons which used to approximate an object. This paper developes a method to eliminate unnecessary sets of polygons, and an efficinet algorithm to compute a minimum distance between two polygons in order to compensate the inherent disadvantage of the algorithm. It takes only a few times iteration to find minimum distance for msot polygons. The correctness of the algortihm are visually tested with a line which connects two points making a global minimum distance of simple convex object(box) and concave object(pipe). The algorithm can find minimum distance between two convex objects made of about 200 polygons respectively less than a second computing time.

• Bulletin of the Korean Mathematical Society
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• v.21 no.2
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• pp.87-89
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• 1984

Let X be a Banach space, and let B(X) (resp. CB(X), K(X), CV(X)) denote the family of all nonvoid (resp. closed bounded, compact, convex) subsets of X. The Kuratowski measure of noncompactness is defined by the mapping .alpha.$_{k}$: B(X).rarw. $R_{+}$ with .alpha.$_{k}$(A) = inf {r>0 vertical bar A can be covered by a finite number of sets with diameter less than r}.an r}.

• Journal of the Korean Mathematical Society
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• v.39 no.1
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• pp.51-60
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• 2002

Some random fixed point theorems for nonexpansive and *-nonexpansive random operators defined on convex and star-shaped sets in a Frechet space are proved. Our work extends recent results of Beg and Shahzad and Tan and Yaun to noncontinuous multivalued random operators, sets analogue to an earlier result of Itoh and provides a random version of a deterministic fixed point theorem due to Singh and Chen.