On the Sum of Squared Logarithms Inequality and Related Inequalities

نویسندگان

  • FOZI M. DANNAN
  • PATRIZIO NEFF
  • CHRISTIAN THIEL
  • F. M. DANNAN
  • P. NEFF
  • C. THIEL
چکیده

We consider the sum of squared logarithms inequality and investigate possible connections with the theory of majorization. We also discuss alternative sufficient conditions on two sets of vectors a,b ∈ R+ so that n ∑ i=1 (logai) n ∑ i=1 (logbi) . Generalizations of some inequalities from information theory are obtained, including a generalized information inequality and a generalized log sum inequality, which states for a,b ∈ R+ and k1, . . . ,kn ∈ [0,∞) : n ∑ i=1 ai log m ∏ s=1 ( ai bi + ks ) log m ∏ s=1 (1+ ks) .

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

General Minkowski type and related inequalities for seminormed fuzzy integrals

Minkowski type inequalities for the seminormed fuzzy integrals on abstract spaces are studied in a rather general form. Also related inequalities to Minkowski type inequality for the seminormed fuzzy integrals on abstract spaces are studied. Several examples are given to illustrate the validity of theorems. Some results on Chebyshev and Minkowski type inequalities are obtained.

متن کامل

On Fejér Type Inequalities for (η1,η2)-Convex Functions

In this paper we find a characterization type result for (η1,η2)-convex functions. The Fejér integral inequality related to (η1,η2)-convex functions is obtained as a generalization of Fejér inequality related to the preinvex and η-convex functions. Also some Fejér trapezoid and midpoint type inequalities are given in the case that the absolute value of the derivative of considered function is (...

متن کامل

On a decomposition of Hardy--Hilbert's type inequality

In this paper, two pairs of new inequalities are given, which decompose two Hilbert-type inequalities.

متن کامل

Studying and Analyzing Regional Inequalities (case study: cities of Ardabil province, Iran 2006 – 2011)

  In this study, to show the inequality between different cities in Ardebil province, 60 developmental indicators in different sections including health care, social, educational, cultural and infrastructural sections have been analyzed through VIKOR model. Moreover, for data analysis and graph and table representation of data Excel, SPSS, and ARC Map 10.1 software was used. For determining va...

متن کامل

On Hadamard and Fej'{e}r-Hadamard inequalities for Caputo $small{k}$-fractional derivatives

In this paper we will prove certain Hadamard and Fejer-Hadamard inequalities for the functions whose nth derivatives are convex by using Caputo k-fractional derivatives. These results have some relationship with inequalities for Caputo fractional derivatives.

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 2016