In the paper, necessary and sufficient conditions are presented for a function and its reciprocal involving a ratio of two gamma functions to be logarithmically completely monotonic, and some known monotonicity and inequality results are generalized and extended.

We consider the existence of optimal parameters for generalized logistic model by least orthogonal absolute deviations, and prove the existence of such optimal solution, under the monotonicity condition on the data.

We describe, in terms of generalized elliptic integrals, the hyperbolic metric of the twice-punctured sphere with one conical singularity of prescribed order. We also give several monotonicity properties of the metric and a couple of applications.

A generalized form of vectorial equilibria is proposed, and, using an abstract monotonicity condition, an existence result is demonstrated. K e y Words: Equilibrium problem, multivalued mapping, pseudomonotone mapping.

In this paper, using a criteria for the monotonicity of quotient two power series, we present some sharp bounds generalized logarithmic operator mean and Heinz by weighted ones classical ones.

In this paper we are concerned with some general properties of scientific hypotheses. We investigate the relationship between the situation when the task is to verify a given hypothesis, and when a scientist has to pick a correct hypothesis from an arbitrary class of alternatives. Both these procedures are based on induction. We understand hypotheses as generalized quantifiers of types 〈1〉 or 〈...

The penalized spline is a popular method for function estimation when the assumption of “smoothness” is valid. In this paper, methods for estimation and inference are proposed using penalized splines under the additional constraints of shape, such as monotonicity or convexity. The constrained penalized spline estimator is shown to have the same convergence rates as the corresponding unconstrain...