By taking into account that the computation of the numerical radius is an optimization problem, we prove, in this paper, several refinements of the numerical radius inequalities for Hilbert space operators. It is shown, among other inequalities, that if A is a bounded linear operator on a complex Hilbert space, thenω(A)≤½√(|| |A|2+|A*|2||+|| |A| |A*|+|A*| |A| ||),where ω(A), ||A||, and |A| are the numerical radius, the usual operator norm, and the absolute value of A, respectively. This inequality provides a refinement of an earlier numerical radius inequality due to Kittaneh, namely,ω(A)≤½(||A||+||A2||)½.Some related inequalities are also discussed. پرونده مقاله

The present paper seeks to establish an approximation of the arithmetic-geometric mean inequality (AM-GM) using a logarithmically concave function. We utilized the specific properties of this class of functions to derive modified versions of the AM-GM inequality as a specific example. These findings present a fresh perspective on the subject. پرونده مقاله