IJPAM: Volume 59, No. 2 (2010)

BEST SIMULTANEOUS APPROXIMATION VIA
KKM-MAPPING METHOD FOR MULTIVALUED MAPPINGS

H.K. Pathak$^1$, Satyaj Tiwari$^2$
$^1$School of Studies in Mathematics
Pt. Ravishankar Shukla University
Raipur (C.G.), 492010, INDIA
e-mail: [email protected]
$^2$Department of Mathematics
Shri Shankaracharya Institute of Professional Management and Technology
P.O. Sejabahar, Mujgahan, Raipur (C.G.), 490021, INDIA
e-mail: [email protected]


Abstract.In this paper, the method of KKM-mapping and the new notion of the measure of quasi-convexity is used to prove result on the best simultaneous approximation for multi-maps. We also give some results on best simultaneous approximation on non convex set. The results of this paper generalized some known results in the literature.

Received: December 29, 2009

AMS Subject Classification: 41A50, 46B40

Key Words and Phrases: best simultaneous approximation, KKM-mapping, quasi-convex multi-function, measure of quasi-convexity and radial cone

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 59
Issue: 2