For fixed s 1 and t1,t2 ∈ (0,1/2) we prove that the inequalities G(t1a + (1− t1)b,t1b+(1− t1)a)A1−s(a,b) > AG(a,b) and G(t2a+(1− t2)b,t2b+(1− t2)a)A1−s(a,b) > L(a,b) hold for all a,b > 0 with a = b if and only if t1 1/2− √ 2s/(4s) and t2 1/2− √ 6s/(6s) . Here G(a,b) , L(a,b) , A(a,b) and AG(a,b) are the geometric, logarithmic, arithmetic and arithmetic-geometric means of a and b , respectively....

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 differentiable, then the monotonicity in parameters p and q of Hf (a, b; p, q) depend on the signs of I1 = (ln f)xy , for variable a and b depend on the sign of I2a = [(ln f)x ln(y/x)]y and I2b = [(ln f)y ln(x/y)...

particulate matters commonly found dispersed in the atmosphere are composed of a large variety of substances. dustfall is the usual index of particles in the size range greater than 10 m. two semi automated so2 sampling units were installed in tehran university campus (from 21 january 1973 to 22 dec. 1974) and gheitarieh area (from 23 august to 23 oct. 1974) hydrogen peroxide method was used fo...

Copulas represent the dependence structure of multivariate distributions in a natural way. In order to generate new copulas from given ones, several proposals found its way into statistical literature. One simple approach is to consider convex-combinations (i.e. weighted arithmetic means) of two or more copulas. Similarly, one might consider weighted geometric means. Consider, for instance, the...

in this study, moisture dependent physical, mechanical and nutritional properties of sesame seed were evaluated. in the moisture range of 4.54–19.27% (d.b.), seed length, width, thickness, arithmetic mean diameter and geometric mean diameter increased linearly from 2.93 to 3.01 mm, 1.74 to 1.78 mm, 0.78 to 0.86 mm, 1.81 to 1.88 mm and 1.58 to 1.66 mm respectively with increase in moisture conte...

Abstract The main purpose of this work is to present essential extensions results in [7] and [8], apply them some special situations. Of particular interest the refinement integral Jensen inequality for vector valued integrable functions. applications related four topics, namely f -divergences information theory (an interesting weighted geometric mean–arithmetic mean obtained as a consequence),...