IJPAM: Volume 78, No. 5 (2012)

BEST APPROXIMATIONS IN UNIFORMLY
CONVEX LINEAR 2-NORMED SPACES

Sivadasan Thirumangalath$^1$, Raji Pilakkat$^2$
Department of Mathematics
University of Calicut
Kerala, 673635, INDIA


Abstract. Let be a smooth, uniformly convex real then the best approximation $ax$ of an element $y\in X\backslash V(x)$ from elements of $V(x)$ (span$\{x\}$), with respect to an element $z\notin V(x,y)$ is characterized in terms of the generalized 2-inner product by the equation $<y-ax,x\vert z>=0$. This idea is extended for best approximation of an element from a subspace of finite dimension.

Received: April 2, 2012

AMS Subject Classification: 41A65, 46C50

Key Words and Phrases: linear 2-normed space, best approximation, uniformly convex, generalised inner product

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 78
Issue: 5