Some New Results of Mitrinović–Cusa’s and Related Inequalities Based on the Interpolation and Approximation Method

In this paper, new refinements and improvements of Mitrinović–Cusa’s and related inequalities are presented. First, we give new polynomial bounds for sinc(x) and cos(x) functions using the interpolation and approximation method. Based on the obtained results of the above two functions, we establish...

Full description

Saved in:
Bibliographic Details
Published in:Journal of mathematics (Hidawi) 2021-01, Vol.2021, p.1-13
Main Authors: Zhang, Lina, Ma, Xuesi
Format: Article
Language:English
Subjects:
Approximation
Inequalities
Inequality
Interpolation
Mathematical analysis
Mathematics
Polynomials
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper, new refinements and improvements of Mitrinović–Cusa’s and related inequalities are presented. First, we give new polynomial bounds for sinc(x) and cos(x) functions using the interpolation and approximation method. Based on the obtained results of the above two functions, we establish new bounds for Mitrinović–Cusa’s, Wilker’s, Huygens’, Wu–Srivastava’s, and Neuman–Sándor’s inequalities. The analysis results show that our bounds are tighter than the previous methods.
ISSN:2314-4629
2314-4785
DOI:10.1155/2021/5595650