This paper discussed the characterizations of uniformly convexity of N -functions. Definition 1. A function M(u): R → R is called an N -function if it has the following properties: (1) M is even, continuous, convex; (2) M(0) = 0 and M(u) > 0 for all u = 0; (3) lim u→0 M(u) u = 0 and lim u→+∞ M(u) u = +∞. The N -function generates the Orlicz spaces. So it is important to analysis it. It is well-...

One of the classical results of the regularity theory of convex functions is the theorem of F. Bernstein and G. Doetsch [1] which states that if a real valued Jensen-convex function defined on an open interval I is bounded from above on a subinterval of I then it is continuous. According to a related result by W. Sierpiński [3], the Lebesgue measurability of a Jensen-convex function implies its...

Some new Jensen’s type inequalities for di¤erentiable log-convex functions of selfadjoint operators in Hilbert spaces under suitable assumptions for the involved operators are given. Applications for particular cases of interest are also provided. 1. Introduction Jensen’s inequality for convex functions is one of the most important result in the Theory of Inequalities due to the fact that many ...

assume that $mathbb{d}$ is the open unit disk. applying ozaki's conditions, we consider two classes of locally univalent, which denote by $mathcal{g}(alpha)$ and $mathcal{f}(mu)$ as follows begin{equation*}  mathcal{g}(alpha):=left{fin mathcal{a}:mathfrak{re}left( 1+frac{zf^{prime prime }(z)}{f^{prime }(z)}right)

Murota (1995) introduced an M-convex function as a quantitative generalization of the set of integral vectors in an integral base polyhedron as well as an extension of valuated matroid over base polyhedron. Just as a base polyhedron can be transformed through a network, an M-convex function can be induced through a network. This paper gives a constructive proof for the induction of an M-convex ...

Quite recently, Murota introduced an M-convex function as a quantitative generalization of the set of integral points in a base polyhedron, as well as an extension of valuated matroid over base polyhedron. Just as a base polyhedron can be transformed through a network, an M-convex function can be induced through a network. This paper gives an algorithmic proof for the induction of an M-convex f...

A binary VCSP is a general framework for the minimization problem of a function represented as the sum of unary and binary cost functions. An important line of VCSP research is to investigate what functions can be solved in polynomial time. Cooper–Živný classified the tractability of binary VCSP instances according to the concept of “triangle,” and showed that the only interesting tractable cas...