A new look at Popoviciu's concept of convexity for functions of two variables

A new look at the Hardy-Littlewood-Pólya inequality of majorization

“…One can characterize the isotonicity of the differential of a convex function by using the concept of 2-box monotonicity, first noticed by Popoviciu [23] in the case when N = 2. See also [10], where the 2-box monotonicity is described in its relationship with another concept due to Popoviciu, 2-box convexity. The natural domains of such functions are the open N -dimensional boxes, that is, the products…”

Some inequalities for a Stancu type operator via (1,1) box convex functions

“…Popoviciu introduced the notion of (m, n) convexity in [9, p. 78]. In [4], S. Gal and P. Niculescu used box convexity of order (m, n) for (m, n) convexity. We will use the terminology introduced in [4] and say that the function f :…”

“…preserves (q, s)-convexity (see [4]). The aim of this article is to prove an inequality of type (8) for operators L α,β n,r,ϕ .…”

An Inequality Involving Some Linear Positive Operators and Box-Convex Functions

“…for any distinct points x 1 , x 2 ∈ I and y 1 , y 2 ∈ I (see also [3]). A (q, s) box-convex function can be characterized via the following lemma.…”

“…In [3], S. Gal and P. Niculescu used box-convexity of order (m, n) for (m, n) convexity. We will use the terminology introduced in [3] and say that the function f :…”