Xiao-Hui Zhang

Sharp Cusa type inequalities with two parameters and their applications

In the article, we present several sharp Cusa type inequalities with two parameters. As applications, some new Shafer-Fink type and Carlson type inequalities for inverse sine and cosine functions, and new inequalities for bivariate means are found.

Sharp One-Parameter Mean Bounds for Yang Mean

We prove that the double inequality holds for all with if and only if and , where , and , , and are the Yang and th one-parameter means of and , respectively.

Sharp Bounds for Toader Mean in terms of Arithmetic and Second Contraharmonic Means

We present the best possible parameters and such that double inequalities , hold for all with , where , and are the arithmetic, second contraharmonic, and Toader means of and , respectively.

Best possible inequalities for the harmonic mean of error function

In this paper, we find the least value r and the greatest value p such that the double inequality erf(Mp(x,y;λ))≤H(erf(x),erf(y);λ)≤erf(Mr(x,y;λ)) holds for all x,y≥1 (or 0<x,y<1) with 0<λ<1, where erf(x)=2π∫0xe−t2dt, and Mp(x,y;λ)=(λxp+(1−λ)yp)1/p (p≠0) and M0(x,y;λ)=xλy1−λ are, respectively, the error function, and weighted power mean.MSC:33B20, 26D15.