Suppose f(x, y) is a positive homogeneous function defined on U(j R+ × R+), call Hf (a, b; p, q) = [ f(a,b) f(aq,bq) ] 1 p−q homogeneous function with two parameters. If f(x, y) is 2nd… (More)

A four-parameter homogeneous mean Fp, q; r, s; a, b is defined by another approach. The criterion of its monotonicity and logarithmically convexity is presented, and three refined chains of… (More)

In the paper, the authors aim to present a double inequality for the integral mean 1 2π ∫ 2π 0 acos 2 θbsin 2 θ d θ in terms of the exponential and logarithmic means. For attaining the goal, by the… (More)

For a,b > 0 with a = b , let NS (a,b) denote the Neuman-Sándor mean defined by NS (a,b) = a−b 2arcsinh a−b a+b and Ap (a,b) , Lp (a,b) denote the r -order power and Lehmer means. Based on our earlier… (More)

In the article, we prove that the double inequalities [Formula: see text] hold for all [Formula: see text] if and only if [Formula: see text] and [Formula: see text] if [Formula: see text], where… (More)

In this paper, the Schur convexity is generalized to Schur f -convexity, which contains the Schur geometrical convexity, harmonic convexity and so on. When f : R+ →R is defined by f (x) = (xm−1)/m if… (More)

We present the best possible parameters p,q ∈ (0,1] such that the double inequality 1 3p2 cos(px)+ 1− 1 3p2 < sin(x) x < 1 3q2 cos(qx)+ 1− 1 3q2 holds for all x ∈ (0,π/2) . As applications, some new… (More)