In this paper we define a functional as a difference between the right-hand side and lefthand side of the refined Boas type inequality using the notation of superquadratic and subquadratic functions and study its prop...In this paper we define a functional as a difference between the right-hand side and lefthand side of the refined Boas type inequality using the notation of superquadratic and subquadratic functions and study its properties, such as exponential and logarithmic convexity. We also, state and prove improvements and reverses of new weighted Boas type inequalities. As a special case of our result we obtain improvements and reverses of the Hardy inequality and its dual inequality. We introduce new Cauchy type mean and prove monotonicity property of this mean.展开更多
基金supported by the Croatian Ministry of Science, Education and Sports (Grant No.117-1170889-0888)supported by the Croatian Ministry of Science,Education and Sports(Grant No.082-0000000-0893)
文摘In this paper we define a functional as a difference between the right-hand side and lefthand side of the refined Boas type inequality using the notation of superquadratic and subquadratic functions and study its properties, such as exponential and logarithmic convexity. We also, state and prove improvements and reverses of new weighted Boas type inequalities. As a special case of our result we obtain improvements and reverses of the Hardy inequality and its dual inequality. We introduce new Cauchy type mean and prove monotonicity property of this mean.
