Functions and Analysis

    

On the Integral Inequality of Some Trigonometric Functions in $mathbb{r}^n$

Authors: Theophilus Agama

In this note, we prove the inequality begin{align}bigg| int limits_{|a_n|}^{|b_n|} int limits_{|a_{n-1}|}^{|b_{n-1}|}cdots int limits_{|a_1|}^{|b_1|}cos bigg(frac{sqrt[4s]{sum limits_{j=1}^{n}x^{4s}_j}}{||vec{a}||^{4s+1}+||vec{b}||^{4s+1}}bigg)dx_1dx_2cdots dx_nbigg| leq frac{bigg|prod_{i=1}^{n}|b_i|-|a_i|bigg|}{|Re(langle a,b angle)|}onumberend{align}and begin{align}bigg|int limits_{|a_n|}^{|b_n|} int limits_{|a_{n-1}|}^{|b_{n-1}|}cdots int limits_{|a_1|}^{|b_1|}sin bigg(frac{sqrt[4s]{sum limits_{j=1}^{n}x^{4s}_j}}{||vec{a}||^{4s+1}+||vec{b}||^{4s+1}}bigg)dx_1dx_2cdots dx_nbigg| leq frac{bigg|prod_{i=1}^{n}|b_i|-|a_i|bigg|}{|Im(langle a,b angle)|}onumberend{align}under some special conditions.

Comments: 6 Pages.

Download: PDF

Submission history

[v1] 2022-07-09 22:55:43

Unique-IP document downloads: 232 times

Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.

comments powered by Disqus