Best approximation for nonconvex set in $q$-normed space

Hemant Kumar Nashine

Department of Mathematics, Raipur Institute of Technology, Mandir Hasaud, Chhatauna, Raipur-492101 (Chhattisgarh), India


Some existence results on best approximation are proved without starshaped subset and affine mapping in the set up of $q$-normed space. First, we consider the closed subset and then weakly compact subsets for said purpose. Our results improve the result of Mukherjee and Som cite{RNM2} and Jungck and Sessa \cite{GJS} and some known results \cite{DOT}, \cite{AL}, \cite{HN} are obtained as consequence. To achieve our goal, we have introduced a property known as ``Property(A)".

AMSclassification. 41A50,47H10,54H25.

Keywords. Best approximation, demiclosed mapping, fixed point, $I$-non\-expan\-sive mapping, $q$-normed space.