CHARACTERIZATION OF INNER PRODUCT SPACE USING DUNKL-WILLIAMS CONSTANT - Widyatma, Leo
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.