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Open Access Research Article

Bessel and Grüss Type Inequalities in Inner Product Modules over Banach -Algebras

AG Ghazanfari1* and SS Dragomir23

Author Affiliations

1 Department of Mathematics, Lorestan University, P.O. Box 465, Khoramabad, Iran

2 School of Engineering and Science, Victoria University, P.O. Box 14428, Melbourne City, MC 8001, Australia

3 School of Computational and Applied Mathematics, University of the Witwatersrand, Private Bag 3 Wits 2050, Johannesburg, South Africa

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Journal of Inequalities and Applications 2011, 2011:562923  doi:10.1155/2011/562923

Published: 14 March 2011

Abstract

We give an analogue of the Bessel inequality and we state a simple formulation of the Grüss type inequality in inner product -modules, which is a refinement of it. We obtain some further generalization of the Grüss type inequalities in inner product modules over proper -algebras and unital Banach -algebras for -seminorms and positive linear functionals.