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  Volume 9, Issue 1, Article 5
On Some Inequalities in Normed Algebras

    Authors: Sever S. Dragomir,  
    Keywords: Normed algebras, Unital algebras, Generalised triangle inequality.  
    Date Received: 24/10/2007  
    Date Accepted: 29/10/2007  
    Subject Codes:

Pri: 46H05; Sec: 47A10.

    Editors: Saburou Saitoh,  

Some inequalities in normed algebras that provides lower and upper bounds for the norm of $ sum_{j=1}^{n}a_{j}x_{j}$ are obtained. Applications for estimating the quantities $ leftVert leftVert x^{-1}rightVert xpm leftVert y^{-1}rightVert yrightVert $ and $ leftVert leftVert y^{-1}rightVert xpm leftVert x^{-1}rightVert yrightVert $ for invertible elements $ x,y$ in unital normed algebras are also given.

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