An Optimal Double Inequality for Means

An Optimal Double Inequality between Seiffert and Geometric Means

Numerical method for solving optimal control problem of the linear differential systems with inequality constraints

In this paper, an efficient method for solving optimal control problems of the linear differential systems with inequality constraint is proposed. By using new adjustment of hat basis functions and their operational matrices of integration, optimal control problem is reduced to an optimization problem. Also, the error analysis of the proposed method is nvestigated and it is proved that the orde...

Optimal Convex Combinations Bounds of Centroidal and Harmonic Means for Weighted Geometric Mean of Logarithmic and Identric Means

In this paper, optimal convex combination bounds of centroidal and harmonic means for weighted geometric mean of logarithmic and identric means are proved. We find the greatest value λ(α) and the least value Δ(α) for each α ∈ (0,1) such that the double inequality: λC(a,b)+(1−λ)H(a,b) < Lα (a,b)I1−α (a,b) < ΔC(a,b)+(1−Δ)H(a,b) holds for all a,b > 0 with a = b. Here, C(a,b), H(a,b) , L(a,b) and I...

An Optimal Double Inequality among the One-Parameter, Arithmetic and Geometric Means

In the present paper, we answer the question: for 0 1    fixed, what are the greatest value   p  and the least value   q  such that the double inequality           , , 1 , p q , J a b A a b G a b J a b       holds for all with ? where for , the one-parameter mean , 0 a b  a b  p R    , p J a b  , , arithmetic mean  A a b     and geometric mean of two positive...

A best-possible double inequality between Seiffert and harmonic means

* Correspondence: [email protected] Department of Mathematics, Huzhou Teachers College, Huzhou, 313000, China Full list of author information is available at the end of the article Abstract In this paper, we establish a new double inequality between the Seiffert and harmonic means. The achieved results is inspired by the papers of Sándor (Arch. Math., 76, 34-40, 2001) and Hästö (Math. ...

Optimal Convex Combination Bounds of Seiffert and Geometric Means for the Arithmetic Mean

We find the greatest value α and the least value β such that the double inequality αT (a,b) + (1−α)G(a,b) < A(a,b) < βT (a,b) + (1− β)G(a,b) holds for all a,b > 0 with a = b . Here T (a,b) , G(a,b) , and A(a,b) denote the Seiffert, geometric, and arithmetic means of two positive numbers a and b , respectively. Mathematics subject classification (2010): 26E60.