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  Volume 7, Issue 5, Article 193
A Generalization of Hölder and Minkowski Inequalities

    Authors: Yılmaz Yilmaz, M. Kemal Özdemır, İhsan Solak,  
    Keywords: Inequalities, Hölder, Minkowski, Sequence algebra, Vector-valued sequence space.  
    Date Received: 29/06/06  
    Date Accepted: 09/11/06  
    Subject Codes:

Pri 26D15, 47A30; Sec 46A45.

    Editors: Kazimierz Nikodem,  

In this work, we give a generalization of Hölder and Minkowski inequalities to normal sequence algebras with absolutely monotone seminorm. Our main result is Theorem 2.1 and Theorem 2.2 which state these extensions. Taking $ F=ell_{1}$ and $ {leftVert {cdot }rightVert }_{F}={leftVert {cdot}rightVert }_{1}$ in both these theorems, we obtain classical versions of these inequalities. Also, using these generalizations we construct the vector-valued sequence space $ Fleft( X,lambda,pright) $ as a paranormed space which is a most general form of the space $ c_{0}left( X,lambda,pright) $ investigated in [6].

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