A central limit theorem and a moderate deviations principle for the ratio of geometric p-generalized arithmetic mean are shown. Also Berry–Esseen-type upper bound on rate convergence in is proved. This has implications probabilistic version question whether inequality between can be reversed or improved up to multiplicative constants. The involved random vectors we study belong class distributi...

The nonlinear solvers in numerical solution of water flow in variably saturated soils are prone to convergence difficulties. Many aspects can give rise to such difficulties, like very dry initial conditions, a steep pressure gradient and great variation of hydraulic conductivity occur across the wetting front during the infiltration of water.  So, the averaging method applied to compute hydraul...

the concept of geometric-arithmetic indices was introduced in the chemical graph theory.these indices are defined by the following general formula:   ( )2( ) uv e g u vu vq qq qga g ,where qu is some quantity that in a unique manner can be associated with the vertex u ofgraph g. in this paper the exact formula for two types of geometric-arithmetic index of vphenylenicnanotube are given.

Using the arithmetic-geometric mean inequality, we give bounds for k-subpermanents of nonnegative n × n matrices F. In the case k = n, we exhibit an n 2-set S whose arithmetic and geometric means constitute upper and lower bounds for per(F)/n!. We offer sharpened versions of these bounds when F has zero-valued entries.

In this paper, the computation of numerical integration using arithmetic mean (AMDCNC), geometric mean (GMDCNC) and harmonic mean (HMDCNC) derivativebased closed Newton cotes quadrature rules are compared with the existing closed Newton cotes quadrature rule (CNC). The comparison shows that, arithmetic mean-based rule gives better solution than the other two rules. This set of quadrature rules ...

Many classical inequalities are just statements about the convexity or concavity of certain (hidden) underlying functions. This is nicely illustrated by Hardy, Littlewood, and Pólya [5] whose Chapter III deals with “Mean values with an arbitrary function and the theory of convex functions,” and by Steele [12] whose Chapter 6 is called “Convexity—The third pillar.” Yet another illustration is th...