New generalization of H. Alzer's inequality

On a New Generalization of Alzer’s Inequality

Let {an}n=1 be an increasing sequence of positive real numbers. Under certain conditions of this sequence we use themathematical induction and the Cauchymean-value theorem to prove the following inequality: an an+m ≤ ( (1/n) ∑n i=1ai (1/(n+m))∑n+m i=1 ai )1/r , where n and m are natural numbers and r is a positive number. The lower bound is best possible. This inequality generalizes the Alzer’s...

A New Generalization of Tchebycheff's Statistical Inequality

A New Generalization of Chebyshev Inequality for Random Vectors

In this article, we derive a new generalization of Chebyshev inequality for random vectors. We demonstrate that the new generalization is much less conservative than the classical generalization. 1 Classical Generalization of Chebyshev inequality The Chebyshev inequality discloses the fundamental relationship between the mean and variance of a random variable. Extensive research works have been...

A New Generalization of Ostrowski Type Inequality on Time Scales

(b− a)‖f ‖∞. (1) The inequality is sharp in the sense that the constant 14 cannot be replaced by a smaller one. For some extensions, generalizations and similar results, see [6, 9, 10, 11, 13, 14] and references therein. The development of the theory of time scales was initiated by Hilger [7] in 1988 as a theory capable to contain both difference and differential calculus in a consistent way. S...

Generalization on Kantorovich Inequality

In this paper, we provide a new form of upper bound for the converse of Jensen’s inequality. Thereby, known estimations of the difference and ratio in Jensen’s inequality are essentially improved. As an application, we also obtain an improvement of Kantorovich inequality.