• Title, Summary, Keyword: S-KKM class

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MIXED VECTOR EQUILIBRIUM-LIKE PROBLEMS IN BANACH SPACES

  • Lee, Byung-Soo;Salahuddin, Salahuddin;Ahmad, M.K.
    • 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.

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Coincidences of composites of u.s.c. maps on h-spaces and applications

  • Park, Seh-Ie;Kim, Hoon-Joo
    • 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.

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COMMENTS ON HOU JICHENG'S "ON SOME KKM TYPE THEOREMS"

  • Park, Se-Hie
    • 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.

A report of 9 unrecorded radiation resistant bacterial species in Korea

  • Kang, Myung-Suk;Srinivasan, Sathiyaraj
    • 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.

COMMENTS ON DING'S EXAMPLES OF FC-SPACES AND RELATED MATTERS

  • Park, Se-Hie
    • 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.