• Communications of the Korean Mathematical Society
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• v.25 no.2
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• pp.303-311
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• 2010

Recently, some authors [3, 4, 11, 12, 15] adopted the concept of the so-called generalized R-KKM maps which are used to rewrite known results in the KKM theory. In the present paper, we show that those maps are simply KKM maps on G-convex spaces. Consequently, results on generalized R-KKM maps follow the corresponding previous ones on G-convex spaces.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.1
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• pp.105-112
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• 2014

In this paper, we first introduce an R-E-KKM map in the E-convex settings, and next we prove an R-E-KKM theorem which generalizes the KKM theorem and the best proximity theorem simultaneously. As applications, a best proximity theorem and a fixed point theorem in E-convex sets are given.

• Bulletin of the Korean Mathematical Society
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• v.53 no.5
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• pp.1363-1371
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• 2016

This paper is concerned with best proximity points for multimaps in normed spaces and in hyperconvex metric spaces. Using the generalized KKM theorem, we deduce new best proximity pair theorems for a family of multimaps with unionly open fibers in normed spaces. And we prove a new best proximity point theorem for quasi-lower semicontinuous multimaps in hyperconvex metric spaces.

• 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.