CHARACTERIZATION OF INNER PRODUCT SPACE USING DUNKL-WILLIAMS CONSTANT
The concept of uniformly convex spaces was introduced by James A. Clarkson in 1935. An example of uniformly convex spaces is an inner product space. Not every normed space is a uniformly convex space. Not every normed space is an inner product space. In a uniformly convex space, we can define the...
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| Format: | Final Project |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/47819 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | The concept of uniformly convex spaces was introduced by James A. Clarkson in
1935. An example of uniformly convex spaces is an inner product space. Not every
normed space is a uniformly convex space. Not every normed space is an inner
product space. In a uniformly convex space, we can define the ‘angle’ between two
vectors as the length of the vector difference. In 1964, Charles F. Dunkl and K.S.
Williams introduced an inequality using the concept of ’angles’ in a uniform convex
spaces. The constant that accompanies the inequality is called the Dunkl-Williams
constant. The Dunkl-Williams constant value for an inner product space is 2. This
final project show if the Dunkl-Williams constant value for a normed space is 2 then
the space is an inner product space. |
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