Cauchy-type means and exponential and logarithmic convexity for superquadratic functions on time scales

Logarithmic Convexity of Area Integral Means for Analytic Functions Ii

For 0 < p < ∞ and −2 ≤ α ≤ 0 we show that the L integral mean on rD of an analytic function in the unit disk D with respect to the weighted area measure (1−|z|) dA(z) is a logarithmically convex function of r on (0, 1).

Logarithmic Convexity of Area Integral Means for Analytic Functions

We show that the L integral mean on rD of an analytic function in the unit disk D with respect to the weighted area measure (1 − |z|) dA(z), where −3 ≤ α ≤ 0, is a logarithmically convex function of r on (0, 1). We also show that the range [−3, 0] for α is best possible.

Logarithmic Convexity for Discrete Harmonic Functions and the Approximation of the Cauchy Problem for Poisson's Equation

Logarithmic convexity type continuous dependence results for discrete harmonic functions defined as solutions of the standard C" piecewise-linear approximation to Laplace's equation are proved. Using this result, error estimates for a regularizaron method for approximating the Cauchy problem for Poisson's equation on a rectangle are obtained. Numerical results are presented.

Logarithmic Convexity of Gini Means

where x and y are positive variables and r and s are real variables. They are also called sum mean values. There has been a lot of literature such as [3, 4, 5, 6, 9, 10, 11, 12, 13, 19, 20, 21] and the related references therein about inequalities and properties of Gini means. The aim of this paper is to prove the monotonicity and logarithmic convexity of Gini means G(r, s;x, y) and related fun...

Research Article On Logarithmic Convexity for Differences of Power Means