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The purpose of this paper is to present some general inequalities for operator concave 2010 Mathematics Subject Classification. Primary 47A63, Secondary 47A64, 15A60.

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In this article, we obtain several new weighted bounds for the numerical radius of a Hilbert space operator. The significance of the obtained results is the way they generalize many existing results in the literature; where certain values of the weights imply some known results, or refinements of these results. In the end, we present some numerical examples that show how our results refine the well known results in the literature, related to this topic.

This paper dedicated to study quadratic maps. We present some new operator equalities and inequalities by using quadratic map in the framework of B (H). Applications for particular case of interest are also provided.