Note on weighted Carleman-type inequality

A double inequality involving the constant e is proved by using an inequality between the logarithmic mean and arithmetic mean. As an application, we generalize the weighted Carleman-type inequality

An inequality involving the constant <i>e</i> and a generalized Carleman-type inequality

In this paper, we establish a double inequality involving the constant e . As an application, we give a generalized Carleman-type inequality

Some Refinements and Generalizations of I. Schur Type Inequalities

Recently, extensive researches on estimating the value of e have been studied. In this paper, the structural characteristics of I. Schur type inequalities are exploited to generalize the corresponding inequalities by variable parameter techniques. Some novel upper and lower bounds for the I. Schur inequality have also been obtained and the upper bounds may be obtained with the help of Maple and automated proving package (Bottema). Numerical examples are employed to demonstrate the reliability of the approximation of these new upper and lower bounds, which improve some known results in the recent literature

Note on weighted Carleman-type inequality

A double inequality involving the constant e is proved by using an inequality between the logarithmic mean and arithmetic mean. As an application, we generalize the weighted Carleman-type inequality