A Remark on Vetrivel’s Existence Theorem on Ky Fan’s Best Approximant
DOI:
https://doi.org/10.5644/SJM.02.1.05Keywords:
Almost affine, almost quasi convex, best approximant, relative almost quasi convex, upper semicontinuous map, open inverse valuesAbstract
Vetrivel (1996) proved an existence theorem on Ky fan's best approximant for multifunction with open inverse values. The object of this paper is to present an improved and extended version of this result.
2000 Mathematics Subject Classification. 41A50, 47H10, 54H25
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References
Ky Fan, Existence of two fixed point theorems of F. E. Browder, Math. Z., 112 (1969), 234–240.
C. D. Horvath, Contractibility and generalized convexity, J. Math. Anal. Appl., 156 (1991), 341–357.
M. Lassonde, Fixed points for Kakutani factorizable multifunctions, J. Math. Anal. Appl., 152 (1990), 46–60.
S. P. Singh, B. Watson and P. Srivastava, Fixed Point Theory and Best Approximation: The KKM-Map Principle, Vol. 424, Kluwer Academic Publishers, 1997.
V. Vetrivel, Existence of Ky Fan’s best approximant for set valued maps, Indian J. Pure Appl. Math., 27 (2) (1996), 173–175.
E. U. Tarafdar and P. J. Watson, A coincidence point theorem and related results, Appl. Math. Lett., 11 (1) (1998), 37–40.
P. Vijayaraju and M. Marudai, Best approximations and fixed points for multivalued mappings, Indian J. Math., 44 (2) (2002), 233–241.
