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Generalized H-KKM Type Theorems in H-Metric Spaces with Applications

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Abstract

The new notions of H-metric spaces and generalized H-KKM mappings were introduced. Some generalized H-KKM type theorems for generalized H-KKM mappings with finitely metrically compactly closed values and finitely metrically compactly open values were established in H-metric spaces. These theorems generalize recent results of Khamsi and Yuan. As applications, some Ky Fan type matching theorems for finitely metrically compactly open covers and finitely metrically compactly closed covers, fixed point theorems and minimax inequality are obtained in H-metric spaces. These results generalize a number of known results in recent literature.

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References

  1. Khamsi M A. KKM and Ky Fan theorem in hyperconvex spaces[J]. J Math Anal Appl,1996,204(2): 298–306.

    Google Scholar 

  2. Yuan X Z. The characterization of generalized metric KKM mappings with open values in hyperconvex metric spaces and some applications[J]. J Math Anal Appl,1999,235(2):315–325.

    Google Scholar 

  3. Yuan X Z. KKM Theory and Applications in Nonlinear Analysis[M]. New York: Marcel Dekker Inc, 1999.

    Google Scholar 

  4. Aronszajn N, Panitchpakdi P. Extensions of uniformly continuous transformations and hyperconvex metric spaces[J]. Pacific J Math,1956,6:405–439.

    Google Scholar 

  5. Bardaro C, Ceppitelli R. Some further generalization of the Knaster-Kuratowski-Mazurkiewicz theorem and minimax inequalities[J]. J Math Anal Appl,1988,132(3):484–490.

    Google Scholar 

  6. Horvath C. Extension and selection theorems in topological spaces with a generalized convexity structure[J]. Ann Fac Sci Toulouse Math,1993,2:253–269.

    Google Scholar 

  7. ZHANG Shi-sheng. Variational Inequalities and Completementarity Problems Theory With Applications[M]. Shanghai: Shanghai Scientific Literature Press, 1991. (in Chinese)

    Google Scholar 

  8. Horvath C. Some result on multivalued mapping and inequalities without convexity[A]. In: Lin, Simons Eds. Nonlinear and Convex Analysis[C]. New York: Marcel Dekker Inc,1987,96–106.

    Google Scholar 

  9. Ding X P, Tan K K. Matching theorems, fixed point theorems and minimax inequalities without convexity[J]. J Austral Math Soc, Ser A,1990,49(1):111–128.

    Google Scholar 

  10. DING Xie-ping. Fixed points minimax inequalities and equilibria of noncompact abstract economies[J]. Taiwanese J Math,1998,2(1):25–55.

    Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Mathematics, Sichuan Normal University, Chengdu, 610066, P R China

    Xie-ping Ding & Fu-quan Xia

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  1. Xie-ping Ding
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  2. Fu-quan Xia
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Ding, Xp., Xia, Fq. Generalized H-KKM Type Theorems in H-Metric Spaces with Applications. Applied Mathematics and Mechanics 22, 1140–1148 (2001). https://doi.org/10.1023/A:1016389031614

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  • DOI: https://doi.org/10.1023/A:1016389031614

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