WebJun 11, 2024 · We focus on the improvements for Young inequality. We give elementary proof for known results by Dragomir, and we give remarkable notes and some comparisons. Finally, we give new inequalities which are extensions and improvements for the inequalities shown by Dragomir. WebIn this paper, we study some improvements of Young type inequalities. We obtain somereverse improvements of Young inequality. Among other results, weshow a refined Young inequality. For v∈[0,1] and a,b >0,then a∇ vb MR(h)a vb, where M v(t)=1+v(1−v) (t−1)2 t and h= b a. And we also obtain a new Young type inequality.
On further refinements for Young inequalities - ResearchGate
WebYoung's inequality for products can be used to prove Hölder's inequality. It is also widely used to estimate the norm of nonlinear terms in PDE theory, since it allows one to estimate a product of two terms by a sum of the same terms raised to a power and scaled. Standard version for conjugate Hölder exponents [ edit] WebMar 21, 2024 · Still, the economy faces downside risks from the weak external environment, reeling from an expected global growth deceleration, rising inflation, and geopolitical turmoil. The recovery is expected to also have overall positive impact on poverty reduction. Last Updated: Mar 21, 2024 track and tower trail
A refinement of Young’s inequality SpringerLink
Webwe focus on the refinements for Young inequality by Dragomir. We give alternative proofs of refined Young inequalities given in [1,2], with elementary calculations. We also show the inequalities we proved in the previous paper [6], give better estimates than ones … WebJan 1, 2024 · The classical Young inequality has a great importance in several fields of mathematics, statistics and other disciplines. Many results were obtained on refinements, generalizations and converses ... WebJan 15, 2015 · Refinements of Young and its reverse inequalities for scalars In this section, we mainly present the improved Young and its reverse inequalities. Lemma 1 Let a, b be two nonnegative real numbers and . (i) If , then (10) (ii) if , then (11) where and . Proof The proof of inequality (11) is similar to that of inequality (10). track and trace 24