5 papers
Optimal bounds for the ratio of differences of quadratic, arithmetic, and harmonic means
Zamina E. Guliyeva, Narmin N. Aliyeva, Yagub N. Aliyev
We determine the optimal constants in inequalities comparing the differences of the quadratic, arithmetic, and harmonic means of nonnegative real numbers. Specifically, we prov…
The Maximum of the Volume of a Cevian Simplex and its Parts
Yagub N. Aliyev
The cevian triangle corresponding to an interior point of a triangle is the triangle determined by the feet of the three cevians concurrent at . It is known that the area of…
The Maximum of the Volume of a Part of a Cevian Simplex
Zamina Guliyeva, Yagub Aliyev
The cevians passing through a point in a simplex create a cevian simplex, which is divided by these cevians into smaller simplices. We consider the problem about the maximum of the…
The dual of Philo's shortest line segment problem
Yagub N. Aliyev
We study the dual of Philo's shortest line segment problem and find the optimal line segments passing through two given points, with a common endpoint, and with the other endpoints…
The extremal values of the ratio of differences of power mean, arithmetic mean, and geometric mean
Yagub Aliyev
In the paper the maximum and the minimum of the ratio of the difference of the arithmetic mean and the geometric mean, and the difference of the power mean and the geometric mean o…