APPLICATIONS OF THE KKM-PRINCIPLE TO PROLLA TYPE THEOREMS

Main Article Content

S. SESSA
S. P. SINGH

Abstract




We prove some theroems of Prolla type [13] using a well known KKM-principle of Ky Fan [6], so generalizing several results known in the literature.




Article Details

How to Cite
SESSA, S., & SINGH, S. P. (1992). APPLICATIONS OF THE KKM-PRINCIPLE TO PROLLA TYPE THEOREMS. Tamkang Journal of Mathematics, 23(4), 279–287. https://doi.org/10.5556/j.tkjm.23.1992.4551
Section
Papers

References

G. Allen, "Variational inequalities, Complementarity problems and duality theorems", J. Math. Anal. Appl., 58 (1977) 1-10.

H. F. Bohnenblust and S. Karlin, "On a theorem of Ville, in: Contributions to the Theory of Games", H. W. Kuhn and A. W. Tucker, Eds., Vol.1, Ann. Math. Studies 24, Princeton Univ. Press (1950), 155-160.

H. Brezis, L. Nirenberg and G. Stampaccl1ia, "A remark on Ky Fan's miinimax principle", Boll. Un. Mat. Ital., 6 (1972), 293-300.

F. Browder, "Coincidence theorems, minimax theorems and variational inequalities", Contemporary Math., 26 (1984), 67-80

K. Fan, "Extensions of two fixed point theorems of F. E. Browder", Math. Z., 112 (1969), 234-240.

K. Fan, "Some properties of convex sets related to fixed point. theorems", Math, Ann., 266 (1984), 519-531.

A. Granas, "KKM-maps and their applications to nonlinear problems ", The Scottish Book, Ed. R. D. Mauldin, Bid :hauser, (1982), 15-61.

C. W. Ha, "Minimax and fixed point theorems", Math. Ann., 248 (1980), 73-77·

C. W. Ha, "Extensions of two fixed point theorems of I

H. Kamiya, "Coincidence theorem and saddle point theorem", Proc. Amer. Math. Soc., 96 (1986), 599-602.

T . C. Lin, "Convex sets, fixed points, variational and minimax inequalities", Bull. Austral. Math. Soc., 34 (1986), 107-117.

T. C. Lin, "Coincidence and fixed points", to appear.

J. B. Prolla, "Fixed point theorems for set-valued mappings and existence of best approximants"Numer Funct. Anal. and Optimiz., 5 (1982-83), 449-455.

M. H. Shih and K. K. Tan, "Covering theorems of convex sets to fixed point theorems, in: Nonlinear and Convex Analysis (Bor-Luh Lin and S. Simons, Eds.) Lecture Notes in Pure and Appl. Math. 107, Marcel Dekker (1987), 235-244.

v.M. Sehgal, S. P. Singh and R. E. Smithson, "Nearest points and some fixed point theorems for weakly compact sets", J. Math. Anal. Appl., 128 (1987), 108-111.