Sharp Inequalities Involving Neuman–sándor and Logarithmic Means

نویسنده

  • EDWARD NEUMAN
چکیده

Sharp bounds for the Neuman-Sándor mean and for the logarithmic mean are established. The bounding quantities are the one-parameter bivariate means called the p-means. In this paper best values of the parameters of the bounding means are obtained. Mathematics subject classification (2010): 26E60, 26D07, 26D20.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Optimal Bounds for Neuman–sándor Mean in Terms of the Convex Combination of Logarithmic and Quadratic or Contra–harmonic Means

In this article, we present the least values α1 , α2 , and the greatest values β1 , β2 such that the double inequalities α1L(a,b)+(1−α1)Q(a,b) < M(a,b) < β1L(a,b)+(1−β1)Q(a,b) α2L(a,b)+(1−α2)C(a,b) < M(a,b) < β2L(a,b)+(1−β2)C(a,b) hold for all a,b > 0 with a = b , where L(a,b) , M(a,b) , Q(a,b) and C(a,b) are respectively the logarithmic, Neuman-Sándor, quadratic and contra-harmonic means of a ...

متن کامل

Neuman–sándor Mean, Asymptotic Expansions and Related Inequalities

The subject of this paper is a systematic study of inequalities of the form (1−μ)M1 +μM3 M2 (1−ν)M1 +νM3 which cover Neuman-Sándor mean and some classical means. Furthermore, following inequalities with optimal parameters were proved: μ 1 H(s,t) +(1−μ) 1 NS(s,t) 1 A(s,t) ν 1 H(s,t) +(1−ν) 1 NS(s,t)

متن کامل

A One–parameter Family of Bivariate Means

A one-parameter family of bivariate means is introduced. Members of the new family of means are derived from a bivariate symmetric mean. It is shown that new means are symmetric in their variables. Several inequalities involving parametric versions of two Seiffert means, the Neuman-Sándor mean, and the logarithmic means are obtained. It is shown that the last four means belong to the family of ...

متن کامل

Stolarsky Means of Several Variables

A generalization of the Stolarsky means to the case of several variables is presented. The new means are derived from the logarithmic mean of several variables studied in [9]. Basic properties and inequalities involving means under discussion are included. Limit theorems for these means with the underlying measure being the Dirichlet measure are established.

متن کامل

Companion Inequalities for Certain Bivariate Means

Sharp companion inequalities for certain bivariate means are obtained. In particular, companion inequalities for those discovered by Stolarsky and Sándor are established.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2013