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An Equivalent Form of the Fundamental Triangle Inequality and its Applications
Fundamental triangle inequality Equivalent form Garfunkel-Bankoff inequality Leuenberger's inequality
2010/1/22
An equivalent form of the fundamental triangle inequality is given. The result is then used to obtain an improvement of the Leuenberger's inequality and a new proof of the Garfunkel-Bankoff inequality...
Generalizations of the Triangle Inequality
Triangle inequality Hilbert space Sum of two Hilbert spaces various operators among Hilbert spaces Reproducing kernel Linear mapping Norm inequality
2008/7/1
Generalizations of the Triangle Inequality.
Reverses of the Continuous Triangle Inequality for Bochner Integral of Vector-Valued Functions in Hilbert Spaces
Triangle inequality Reverse inequality Hilbert spaces Bochner integral
2008/6/27
Some reverses of the continuous triangle inequality for Bochner integral of vector-valued functions in Hilbert spaces are given. Applications for complex-valued functions are provided as well.
Reverses of the Triangle Inequality in Banach Spaces
Reverse triangle inequality Hilbert spaces Banach spaces Bochner integral
2008/6/27
Recent reverses for the discrete generalised triangle inequality and its continuous version for vector-valued integrals in Banach spaces are surveyed. New results are also obtained. Particular instanc...
In this paper, we show the triangle inequality and its reverse inequality in quasi-Banach spaces.