PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.)
Vol. 52(66), pp. 77--85 (1992)
On best simultaneous approximation
S.V.R. NaiduDepartment of Applied Mathematics, A.U.P.G. Centre Nuzvid 521201, India
Abstract: For nonempty subsets $F$ and $K$ of a nonempty set $V$ and a real valued function $f$ on $X\times X$ the notion of $f$-best simultaneous approximation to $F$ from $K$ is introduced as an extension of the known notion of best simultaneous approximation in normed linear spaces. The concept of uniformly quasi-convex function on a vector space is also introduced. Sufficient conditions for the existence and uniqueness of $f$-best simultaneous approximation are obtained.
Classification (MSC2000): 41A28, 41A50, 41A52; 54H99, 46A99
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