Generalizations of the Triangle Inequality

摘要

The triangle inequality is well-known and fundamental. Since the 8th General Inequalities meeting in Hungary (September 15-21, 2002), the author has been considering an idea that as triangle inequality, the inequality may be more suitable. The triangle inequality will be naturally generalized for some natural sum of any two members of any two Hilbert spaces . We shall introduce a natural sum Hilbert space for two arbitrary Hilbert spaces.