# 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

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topLai-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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- [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. Zbl0858.47033
- [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. Zbl0829.49002
- [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] 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] S. Park and K.S. Jeong, A general coincidence theorem on contractible space, to appear. Zbl0876.47038

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