scholarly journals A double inequality for the combination of Toader mean and the arithmetic mean in terms of the contraharmonic mean

2016 ◽  
Vol 99 (113) ◽  
pp. 237-242 ◽  
Author(s):  
Wei-Dong Jiang ◽  
Feng Qi
Keyword(s):  
Arithmetic Mean ◽  
Double Inequality ◽  
Toader Mean ◽  
Contraharmonic Mean

We find the greatest value ? and the least value ? such that the double inequality C(?a +(1-?)b, ?b + (1-?)a) < ?A(a,b) + (1-?)T(a, b)< C(?a + (1-?)b, ?b + (1-?)a) holds for all ? ? (0,1) and a, b > 0 with a ? b, where C(a,b), A(a,b), and T(a,b) denote respectively the contraharmonic, arithmetic, and Toader means of two positive numbers a and b.

scholarly journals Bounds for Combinations of Toader Mean and Arithmetic Mean in Terms of Centroidal Mean

2013 ◽  
Vol 2013 ◽  
pp. 1-4
Author(s):  
Wei-Dong Jiang
Keyword(s):  
Arithmetic Mean ◽  
Double Inequality ◽  
Toader Mean

The authors find the greatest valueλand the least valueμ, such that the double inequalityC¯(λa+(1-λb),λb+(1-λ)a)<αA(a,b)+(1-α)T(a,b)<C¯(μa+(1-μ)b,μb+(1-μ)a)holds for allα∈(0,1)anda,b>0witha≠b, whereC¯(a,b)=2(a2+ab+b2)/3(a+b),A(a,b)=(a+b)/2, andTa,b=2/π∫0π/2a2cos2θ+b2sin2θdθdenote, respectively, the centroidal, arithmetic, and Toader means of the two positive numbersaandb.

scholarly journals Sharp Bounds for Seiffert Mean in Terms of Contraharmonic Mean

2012 ◽  
Vol 2012 ◽  
pp. 1-6 ◽  
Author(s):  
Yu-Ming Chu ◽  
Shou-Wei Hou
Keyword(s):  
Sharp Bounds ◽  
Double Inequality ◽  
Seiffert Mean ◽  
Contraharmonic Mean

We find the greatest valueαand the least valueβin(1/2,1)such that the double inequalityC(αa+(1-α)b,αb+(1-α)a)<T(a,b)<Cβa+1-βb,βb+(1-βa)holds for alla,b>0witha≠b. Here,T(a,b)=(a-b)/[2 arctan((a-b)/(a+b))]andCa,b=(a2+b2)/(a+b)are the Seiffert and contraharmonic means ofaandb, respectively.

scholarly journals Sharp Generalized Seiffert Mean Bounds for Toader Mean

2011 ◽  
Vol 2011 ◽  
pp. 1-8 ◽  
Author(s):  
Yu-Ming Chu ◽  
Miao-Kun Wang ◽  
Song-Liang Qiu ◽  
Ye-Fang Qiu
Keyword(s):  
Elliptic Integrals ◽  
Double Inequality ◽  
Seiffert Mean ◽  
Toader Mean ◽  
Complete Elliptic Integrals

Forp∈[0,1], the generalized Seiffert mean of two positive numbersaandbis defined bySp(a,b)=p(a-b)/arctan[2p(a-b)/(a+b)],  0<p≤1,  a≠b;  (a+b)/2,  p=0,  a≠b;  a,  a=b. In this paper, we find the greatest valueαand least valueβsuch that the double inequalitySα(a,b)<T(a,b)<Sβ(a,b)holds for alla,b>0witha≠b, and give new bounds for the complete elliptic integrals of the second kind. Here,T(a,b)=(2/π)∫0π/2a2cos⁡2θ+b2sin⁡2θdθdenotes the Toader mean of two positive numbersaandb.

scholarly journals Note on weighted Carleman-type inequality

2005 ◽  
Vol 2005 (3) ◽  
pp. 475-481 ◽  
Author(s):  
Chao-Ping Chen ◽  
Wing-Sum Cheung ◽  
Feng Qi
Keyword(s):  
Type Inequality ◽  
Arithmetic Mean ◽  
Logarithmic Mean ◽  
Double Inequality ◽  
Carleman Type

A double inequality involving the constanteis proved by using an inequality between the logarithmic mean and arithmetic mean. As an application, we generalize the weighted Carleman-type inequality.

scholarly journals The Optimal Upper and Lower Power Mean Bounds for a Convex Combination of the Arithmetic and Logarithmic Means

2010 ◽  
Vol 2010 ◽  
pp. 1-9 ◽  
Author(s):  
Wei-Feng Xia ◽  
Yu-Ming Chu ◽  
Gen-Di Wang
Keyword(s):  
Convex Combination ◽  
Arithmetic Mean ◽  
Power Mean ◽  
Logarithmic Mean ◽  
Positive Real ◽  
Lower Power ◽  
Double Inequality ◽  
Logarithmic Means

Forp∈ℝ, the power meanMp(a,b)of orderp, logarithmic meanL(a,b), and arithmetic meanA(a,b)of two positive real valuesaandbare defined byMp(a,b)=((ap+bp)/2)1/p, forp≠0andMp(a,b)=ab, forp=0,L(a,b)=(b-a)/(log⁡b-log⁡a), fora≠bandL(a,b)=a, fora=bandA(a,b)=(a+b)/2, respectively. In this paper, we answer the question: forα∈(0,1), what are the greatest valuepand the least valueq, such that the double inequalityMp(a,b)≤αA(a,b)+(1-α)L(a,b)≤Mq(a,b)holds for alla,b>0?

scholarly journals Perbandingan Algoritma Contraharmonic Mean Filter dan Arithmetic Mean Filter untuk Mereduksi Exponential Noise

2020 ◽  
Vol 5 (2) ◽  
pp. 107
Author(s):  
Mhd Furqan ◽  
Sriani Sriani ◽  
Yuli Kartika Siregar
Keyword(s):  
Image Analysis ◽  
Image Quality ◽  
Mean Square Error ◽  
Signal To Noise Ratio ◽  
Arithmetic Mean ◽  
Mean Square ◽  
Signal To Noise ◽  
Contraharmonic Mean ◽  
Mean Filter ◽  
Filtering Technique

Noise in the image caused a decrease in image quality, so that the image will look dirty and spots appear on the resulting image. Noise also results in reduced information on the resulting image so that noise limits valuable information when image analysis is performed. Filtering technique is one way to overcome noise. The filtering technique used in this study is using the Contraharmonic Mean Filter algorithm and the Arithmetic Mean Filter algorithm with the type of noise used to reduce the Exponential Noise. The results of the two algorithms show that the Arithmetic Mean Filter algorithm is a better algorithm to reduce the Exponential Noise compared to the Contraharmonic Mean Filter algorithm which is proven based on the value of MSE (Mean Square Error) and PSNR (Peak Signal-to-Noise Ratio).

scholarly journals Sharp Bounds for Neuman Means by Harmonic, Arithmetic, and Contraharmonic Means

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Zhi-Jun Guo ◽  
Yu-Ming Chu ◽  
Ying-Qing Song ◽  
Xiao-Jing Tao
Keyword(s):  
Convex Combination ◽  
Arithmetic Mean ◽  
Harmonic Mean ◽  
Sharp Bounds ◽  
Contraharmonic Mean

We give several sharp bounds for the Neuman meansNAHandNHA(NCAandNAC) in terms of harmonic meanH(contraharmonic meanC) or the geometric convex combination of arithmetic meanAand harmonic meanH(contraharmonic meanCand arithmetic meanA) and present a new chain of inequalities for certain bivariate means.

scholarly journals New Modification on Heun’s Method Based on Contraharmonic Mean for Solving Initial Value Problems with High Efficiency

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Abushet Hayalu Workie
Keyword(s):  
Initial Value Problems ◽  
High Performance ◽  
High Efficiency ◽  
Arithmetic Mean ◽  
Initial Condition ◽  
Initial Value ◽  
Euler’S Method ◽  
Contraharmonic Mean ◽  
The Stability ◽  
Tangent Slope

In this paper, small modification on Improved Euler’s method (Heun’s method) is proposed to improve the efficiency so as to solve ordinary differential equations with initial condition by assuming the tangent slope as an average of the arithmetic mean and contra-harmonic mean. In order to validate the conclusion, the stability, consistency, and accuracy of the system were evaluated and numerical results were presented, and it was recognized that the proposed method is more stable, consistent, and accurate with high performance.

Sign in / Sign up

Export Citation Format

Share Document