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

Lai-Jiu Lin; Ching-Jung Ko; Sehie Park

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (1998)

  • Volume: 18, Issue: 1-2, page 69-85
  • ISSN: 1509-9407

Abstract

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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.

How to cite

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Lai-Jiu Lin, Ching-Jung Ko, and Sehie Park. "Coincidence theorems for set-valued maps with g-kkm property on generalized convex space." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 18.1-2 (1998): 69-85. <http://eudml.org/doc/275962>.

@article{Lai1998,
abstract = {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.},
author = {Lai-Jiu Lin, Ching-Jung Ko, Sehie Park},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {coincidence theorem; KKM property minimax theorem; G(eneralized)-convex space; map with G-KKM property; fixed point; best approximation; minimax theorem; G-KKM spaces; KKM property},
language = {eng},
number = {1-2},
pages = {69-85},
title = {Coincidence theorems for set-valued maps with g-kkm property on generalized convex space},
url = {http://eudml.org/doc/275962},
volume = {18},
year = {1998},
}

TY - JOUR
AU - Lai-Jiu Lin
AU - Ching-Jung Ko
AU - Sehie Park
TI - Coincidence theorems for set-valued maps with g-kkm property on generalized convex space
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 1998
VL - 18
IS - 1-2
SP - 69
EP - 85
AB - 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.
LA - eng
KW - coincidence theorem; KKM property minimax theorem; G(eneralized)-convex space; map with G-KKM property; fixed point; best approximation; minimax theorem; G-KKM spaces; KKM property
UR - http://eudml.org/doc/275962
ER -

References

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  1. [1] J.P. Aubin., A Cellina, Differential Inclusions, Spriger-Verlag, Berlin Heidelberg 1984. Zbl0538.34007
  2. [2] T.H. Chang and C.L. Yen, KKM propperty and fixed point theorems, J. Math. Anal. Appl. to appear. 
  3. [3] A. Granas and F.C. Liu, Coincidences for set-valued maps and minimax inequalities, J. Math. Pures Appl. 65 (1986), 119-148. Zbl0659.49007
  4. [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. [5] L.J. Lin, A generalization of Ky Fan matching theorem to G-convex space for admissible multifunction, to appear. 
  6. [6] M. Lassonde, On the use of KKM multifunctions in fixed point theory and related topics, J. Math. Anal. Appl. 97 (1983), 151-201. Zbl0527.47037
  7. [7] J. Von Neumann, Ueler ein okonomisches gleichungssystm wnd eine verallemeineruny des biorwerscher Fixpwnktsatzes, Eegebnisse eines mathematischen kollogiws, 8 (1935), 73-83. 
  8. [8] S. Park, Acyclic maps, minimax inequality and fixed points, Nonlinear Analysis, Theory. Methods and Applications 24 (1995), 1549-1554. Zbl0858.47033
  9. [9] S. Park and H. Kim, Coincidence theorems for admissible multifunctions on generalized convex space, J. Math. Anal. Appl. (1995). 
  10. [10] S. Park, Foundations of the KKM theory via coincidences of composites of upper semicontinuous maps, J. Korean. Math. Soc. 31 (1994), 493-519. Zbl0829.49002
  11. [11] S. Park and H. Kim, Foundations of the KKM theory on generalized convex spaces, J. Math. Anal. Appl. 209 (1997), 551-571. Zbl0873.54048
  12. [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. Zbl0806.47053
  13. [13] S. Park and K.S. Jeong, A general coincidence theorem on contractible space, to appear. Zbl0876.47038

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