Interpolating the arithmetic–geometric mean inequality and its operator version

Improved logarithmic-geometric mean inequality and its application

In this short note, we present a refinement of the logarithmic-geometric mean inequality. As an application of our result, we obtain an operator inequality associated with geometric and logarithmic means.

Jensen’s Operator Inequality and Its Converses

where φ : A → B(H) is a unital completely positive linear map from a C-algebra A to linear operators on a Hilbert space H, and x is a self-adjoint element in A with spectrum in I. Subsequently M. D. Choi [3] noted that it is enough to assume that φ is unital and positive. In fact, the restriction of φ to the commutative C-algebra generated by x is automatically completely positive by a theorem ...

Weighted Inequalities for the Sawyer Two-dimensional Hardy Operator and Its Limiting Geometric Mean Operator

We consider T f = ∫ x1 0 ∫ x2 0 f (t1, t2)dt1dt2 and a corresponding geometric mean operator G f = exp(1/x1x2) ∫ x1 0 ∫ x2 0 log f (t1, t2)dt1dt2. E. T. Sawyer showed that the Hardy-type inequality ‖T f ‖Lq u ≤ C‖ f ‖Lp v could be characterized by three independent conditions on the weights. We give a simple proof of the fact that if the weight v is of product type, then in fact only one condit...

Max-Min averaging operator: fuzzy inequality systems and resolution

 Minimum and maximum operators are two well-known t-norm and s-norm used frequently in fuzzy systems. In this paper, two different types of fuzzy inequalities are simultaneously studied where the convex combination of minimum and maximum operators is applied as the fuzzy relational composition. Some basic properties and theoretical aspects of the problem are derived and four necessary and suffi...

An Operator Extension of Bohr's inequality