• Bulletin of the Korean Mathematical Society
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• v.42 no.4
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• pp.739-756
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• 2005

The paper presents new collectively fixed point theorems, minimax and quasi-variational inequalities for maps in the S-KKM class.

• Communications of the Korean Mathematical Society
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• v.25 no.3
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• pp.491-495
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• 2010

In a paper by Hou Jicheng, On some KKM type theorems, Advaces in Mathematics 36 (2007), no. 1, 86-88, the author claimed that some previous KKM type theorems are false by giving a counterexample. In the present paper, we show that the counterexample does not work and, consequently, the results are correct. Moreover, we claim that the artificial concept like transfer compactly closed-valued maps can be destroyed. Finally, we introduce a theorem generalizing the main target of Hou.

• Nonlinear Functional Analysis and Applications
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• v.26 no.1
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• pp.93-104
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• 2021

In this paper, we present a fixed point theorem for a family of generalized condensing multimaps which have ranges of the Zima-Hadžić type in Hausdorff KKM uniform spaces. It extends Himmelberg et al. type fixed point theorem. As applications, we obtain some new collective fixed point theorems for various type generalized condensing multimaps in abstract convex uniform spaces.

• East Asian mathematical journal
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• v.25 no.4
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• pp.505-516
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• 2009

In this paper, we consider a new class of generalized mixed vector equilibrium-like problems in Banach spaces. By using Fan-KKM Theorem and Nadler's Theorem, we prove the existence theorem of solution for this class of generalized mixed vector equilibrium-like problems.

• Journal of Species Research
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• v.6 no.2
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• pp.91-100
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• 2017

Five bacterial strains, ES10-3-3-1, KKM10-2-2-1, Ant11, JM10-4-1-3, and KMS4-11 assigned to the genus Deinococcus were isolated from soil samples collected from Namyangju-si in Gyeonggi-do, Gangnam-gu and Dongdaemun-gu in Seoul, Korea. In addition, four bacterial strains, KKM10-2-7-2, JM10-2-5, JM10-2-6-2, and KKM10-2-3 assigned to the genus Hymenobacter were isolated from soil samples collected from Gangnam-gu and Dongdaemun-gu in Seoul, in South Korea. The five Deinococcus species were Gram-stain positive, pink-pigmented, and short-rod or coccus shaped. The four Hymenobacter species were Gram-stain negative, red-pigmented, and short-rod shaped. Phylogenetic analysis based on 16S rRNA gene sequences revealed that strains ES10-3-3-1, KKM10-2-2-1, Ant11, JM10-4-1-3, and KMS4-11 were most closely related to Deinococcus citri $NCCP-154^T$ (with 99.8% similarity), Deinococcus grandis DSM $12784^T$ (99.0%), Deinococcus marmoris DSM $12784^T$ (98.8%), Deinococcus claudionis $PO-04-19-125^T$ (98.7%), and Deinococcus radioresistens $8A^T$ (99.8%), respectively. KKM10-2-7-2, JM10-2-5, JM10-2-6-2, and KKM10-2-3 were most closely related to Hymenobacter algoricola $VUG-A23a^T$ (99.1% similarity), Hymenobacter elongatus $VUG-A112^T$ (99.1% similarity), Hymenobacter gelipurpurascens $Txg1^T$ (99.1% similarity), and Hymenobacter psychrotolerans $Tibet-IIU11^T$ (99.3% similarity), respectively. These nine species have never been reported in Korea; thus, five Deinococcus species are reported in the family Deinococcaceae, order Deinococcales, class Deinococci, phylum Deinococcus-Thermus and four Hymenobacter species are reported in the family Cytophagaceae, order Cytophagales, class Cytophagia, phylum Bacteroidetes.

• Journal of the Korean Mathematical Society
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• v.31 no.3
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• pp.493-519
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• 1994

In the KKM theory, there exist mutually equivalent fundamental theorems from which most of the other important results in the theory can be deduced. We give such fundamental theorems related to composites of upper semicontinuous (u.s.c.) multifunctions in a very large class.

• Journal of the Korean Mathematical Society
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• v.32 no.2
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• pp.251-264
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• 1995

Applications of the classical Knaster-Kuratowski-Mazurkiewicz (si-mply, KKM) theorem and the fixed point theory of multifunctions defined on convex subsets of topological vector spaces have been greatly improved by adopting the concept of convex spaces due to Lassonde [L1]. In this direction, the first author [P5] found that certain coincidence theorems on a large class of composites of upper semicontinuous multifunctions imply many fundamental results in the KKM theory.

• East Asian mathematical journal
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• v.26 no.3
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• pp.389-395
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• 2010

In this paper, a class of g-demi-pseudomonotone mappings is introduced and the solvability of a class of generalized vector F-complementarity problems with the mappings in Banach spaces is considered.

• Communications of the Korean Mathematical Society
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• v.27 no.1
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• pp.137-148
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• 2012

Recently Ding [4, 5, 8] gives examples of his FC-spaces which are not L-spaces due to Ben-El-Mechaiekh et al. [1]. We show that they are actually L-spaces. We also clarify that all statements in [5] can be stated in corrected and generalized forms for the class of abstract convex spaces beyond FC-spaces.