Note on Aczel-type inequality and Bellman-type inequality

A New Generalized Gronwall-Bellman Type Inequality

Note on an Iyengar type inequality

Using Hayashi's inequality, an Iyengar type inequality for functions with bounded second derivative is obtained. This result improves a similar result from [N. Elezovi´c, J. Pečari´c, Steffensen's inequality and estimates of error in trapezoidal rule, Appl. In 1938 Iyengar proved the following inequality in [1]: Theorem 1. Let function f be differentiable on [a, b] and | f (x)| ≤ M. Then 1 b − ...

A Note on Perelman’s Lyh Type Inequality

We give a proof to the Li-Yau-Hamilton type inequality claimed by Perelman on the fundamental solution to the conjugate heat equation. The rest of the paper is devoted to improving the known differential inequalities of Li-Yau-Hamilton type via monotonicity formulae.

Note on weighted Carleman-type inequality

In (1.2), letting p → ∞, then the following Carleman inequality [6, page 249] is deduced: ∞ ∑ n=1 ( a1a2 ···an )1/n < e ∞ ∑ n=1 an, (1.3) where an ≥ 0 for n∈N and 0 < ∑∞ n=1 an <∞. The constant e is the best possible. Carleman’s inequality (1.3) was generalized in [6, page 256] by Hardy as follows. Let an ≥ 0, λn > 0, Λn = ∑n m=1 λm for n∈N, and 0 < ∑∞ n=1 λnan <∞, then ∞ ∑ n=1 λn ( a1 1 a λ2 2...

The Brunn-Minkowski-Type Inequality