NettetBy using Hölder’s inequality (2), we obtain since Using induction hypothesis and inequality (30), we can get Hence, this completes the proof. (2) The Proof of (28) is similar to the proof of (27). Clearly when , inequality (28) becomes Hölder’s inequality (23). Now, suppose that (28) holds for some integer . NettetIn 1994 Hovenier [2] proved sharpening Cauchy’s Inequality; and in 1995 Abramovich, Mond, and Pecaric [1] generalized the result of Hovenier to Holder’s Inequality. Finally, it is vital to mention that Holder’s Inequality is used to prove Minkowski’s Inequality. In this Note we will give an easier proof of Holder’s Inequality.

Moment Inequalities and Their Application - Harvard University

NettetExtensions of Hölder's inequality and its applications in Ostrowski inequality Authors: Fei Yan Hong-Ying Yue Abstract In this paper, we present several new extensions and … NettetEXTENSION OF HOLDER'S INEQUALITY (I) E.G. KWON A continuous form of Holder's inequality is established and used to extend the inequality of Chuan on the … boys parts show

A Note on H¨older’s Inequality

NettetThe Prékopa–Leindler inequality is useful in the theory of log-concave distributions, as it can be used to show that log-concavity is preserved by marginalization and independent summation of log-concave distributed random variables. Nettet(Holder's inequality applies because f ∈ L p ( R) implies f p ′ ∈ L p / p ′ ( R), and p ′ p + p ′ q = 1 .) As a result, f g ∈ L p ′ ( R). Apply Holder's inequality again to get the very first inequality up above. Hope this will help you. Share Cite Follow edited Oct 20, 2024 at 2:29 roxas3582 450 6 11 answered Aug 8, 2011 at 5:10 http://mia.ele-math.com/volume/24 boys paper dolls