Abstract In the present paper we are concerned with problem of separation two given functions by an increasing (decreasing) function or a bounded variation. context variation give approaches. The first one concerns respect to classical order in set real numbers, and this allow us new concept involving functions. This approach fact leads unusual phenomenon, namely joint forces these be essential...

Let -----. For an analytic self-map ---  of --- , Let --- be the composition operator with composite map ---  so that ----. Let ---  be a bounded analytic function on --- . The weighted composition operator ---  is defined by --- . Suppose that ---  is the Hardy space, consisting of all analytic functions defined on --- , whose Maclaurin cofficients are square summable. .....

Estimation in truncated parameter space is one of the most important features in statistical inference, because the frequently used criterion of unbiasedness is useless, since no unbiased estimator exists in general. So, other optimally criteria such as admissibility and minimaxity have to be looked for among others. In this paper we consider a subclass of the exponential families of distributi...

We propose a quartic function to represent a family of continuous quality loss functions. Depending on the choice of its parameters the shape of this function within the specification limits can be either symmetric or asymmetric, and it can be either similar to the ubiquitous quadratic loss function or somewhat closer to the conventional step function. We examine this family of loss functions i...

We generalize a result of Gao and Xu [4] concerning the approximation of functions of bounded variation by linear combinations of a fixed sigmoidal function to the class of functions of bounded φ-variation (Theorem 2.7). Also, in the case of one variable, [1: Proposition 1] is improved. Our proofs are similar to that of [4].

Extending Itô’s formula to non-smooth functions is important both in theory and applications. One of the fairly general extensions of the formula, known as Meyer-Itô, applies to one dimensional semimartingales and convex functions. There are also satisfactory generalizations of Itô’s formula for diffusion processes where the Meyer-Itô assumptions are weakened even further. We study a version of...

A companion for the Ostrowski and the generalised trapezoid inequalites for various classes of functions, including functions of bounded variation, Lipschitzian, convex and absolutely continuous functions is established. Applications for weighted means are also given.

Loss-averse behavior makes the newsvendors avoid the losses more than seeking the probable gains as the losses have more psychological impact on the newsvendor than the gains. In economics and decision theory, the classical newsvendor models treat losses and gains equally likely, by disregarding the expected utility when the newsvendor is loss-averse. Moreover, the use of unbounded utility to m...

Let $X$ be a  Banach  space, $Csubset X$  be  a  closed  convex  set  included  in  a well-based cone $K$, and also let $sigma_C$ be the support function which is defined on $C$. In this note, we first study the existence of a  bounded base for the cone $K$, then using the obtained results, we find some geometric conditions for the set  $C$,  so that ${mathop{rm int}}(mathrm{dom} sigma_C) neqem...

t− a if a ≤ t ≤ x t− b if x < t ≤ b . In the last decade, many authors (see for example [2] and the references therein) have extended the above result for different classes of functions defined on a compact interval, including: functions of bounded variation, monotonic functions, convex functions, n-time differentiable functions whose derivatives are absolutely continuous or satisfy different c...