1 Introduction and preliminaries
2 Some technical lemmas
3 Extensions of Sherman’s inequality
4 Applications in information theory
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Hellinger discrimination:$$h^{2} ( \mathbf{u},\mathbf{v} ) =\frac{1}{2}\sum _{i=1}^{m} ( \sqrt{u_{i}}- \sqrt{v_{i}} ) ^{2}. $$
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\(\boldsymbol{\chi^{2}}\)-divergence:$$D_{\chi^{2}} ( \mathbf{u},\mathbf{v} ) =\sum_{i=1}^{m} \frac { ( u_{i}-v_{i} ) ^{2}}{v_{i}}. $$
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Triangular discrimination:$$\Delta ( \mathbf{u},\mathbf{v} ) =\sum_{i=1}^{m} \frac{ ( u_{i}-v_{i} ) ^{2}}{u_{i}+v_{i}}. $$