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

• Autorzy: Lai-Jiu Lin , Ching-Jung Ko , Sehie Park
• 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.

Słowa kluczowe

EN

coincidence theorem; KKM property minimax theorem

Kategorie tematyczne

• 47H10: Fixed-point theorems
• 54H25: Fixed-point and coincidence theorems

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae, Differential Inclusions, Control and Optimization
• Rocznik: 1998
• Tom: 18
• Numer: 1-2
• Strony: 69-85

Daty

wydano

1998

otrzymano

1998-12-02

Twórcy

autor

Lai-Jiu Lin

• Department of Mathematics, National Changhua University of Education, Changhua, Taiwan, Republic of China

autor

Ching-Jung Ko

• Department of Mathematics, National Changhua University of Education, Changhua, Taiwan, Republic of China

autor

Sehie Park

• 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.