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1998 | 18 | 1-2 | 69-85
Tytuł artykułu

Coincidence theorems for set-valued maps with g-kkm property on generalized convex space

Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, a set-valued mapping with G-KKM property is defined and a generalization of minimax theorem for set-valued maps with G-KKM property on generalized convex space is established. As a consequence of this results we verify the coincidence theorem for set-valued maps with G-KKM property on G-convex space. Finally, we apply our results to the best approximation problem and fixed point problem.
Twórcy
autor
  • Department of Mathematics, National Changhua University of Education, Changhua, Taiwan, Republic of China
  • Department of Mathematics, National Changhua University of Education, Changhua, Taiwan, Republic of China
autor
  • Department of Mathematics, Seoul National University, Seoul 151-742 Republic of Korea
Bibliografia
  • [1] J.P. Aubin., A Cellina, Differential Inclusions, Spriger-Verlag, Berlin Heidelberg 1984.
  • [2] T.H. Chang and C.L. Yen, KKM propperty and fixed point theorems, J. Math. Anal. Appl. to appear.
  • [3] A. Granas and F.C. Liu, Coincidences for set-valued maps and minimax inequalities, J. Math. Pures Appl. 65 (1986), 119-148.
  • [4] C. Horvath, Some results on multivalued mappings and inequalities without convexity in nonlinear and convex analysis, (Eds. B.L. Lin and S. Simons), pp. 99-106 (Marcel Dekker, 1989).
  • [5] L.J. Lin, A generalization of Ky Fan matching theorem to G-convex space for admissible multifunction, to appear.
  • [6] M. Lassonde, On the use of KKM multifunctions in fixed point theory and related topics, J. Math. Anal. Appl. 97 (1983), 151-201.
  • [7] J. Von Neumann, Ueler ein okonomisches gleichungssystm wnd eine verallemeineruny des biorwerscher Fixpwnktsatzes, Eegebnisse eines mathematischen kollogiws, 8 (1935), 73-83.
  • [8] S. Park, Acyclic maps, minimax inequality and fixed points, Nonlinear Analysis, Theory. Methods and Applications 24 (1995), 1549-1554.
  • [9] S. Park and H. Kim, Coincidence theorems for admissible multifunctions on generalized convex space, J. Math. Anal. Appl. (1995).
  • [10] S. Park, Foundations of the KKM theory via coincidences of composites of upper semicontinuous maps, J. Korean. Math. Soc. 31 (1994), 493-519.
  • [11] S. Park and H. Kim, Foundations of the KKM theory on generalized convex spaces, J. Math. Anal. Appl. 209 (1997), 551-571.
  • [12] S. Park, S.P. Singh and B. Watson, Some fixed point theorems for composites of acyclic maps, Proc. Amer. Math. Soc. 121 (1994), 1151-1158.
  • [13] S. Park and K.S. Jeong, A general coincidence theorem on contractible space, to appear.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-div18i1-2n6bwm
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