We establish extremal values of a solution y of a second-order initial value problem as the coefficients vary in a nonconvex set. These results extend earlier work by M. Essen in particular by allowing a coefficient in the second derivative expression.

A convexity structure satisfies the separation property 5'4 if any two disjoint convex sets extend to complementary half-spaces. This property is investigated for alignment spaces, n-ary convexities, and graphs. In particular, it is proven that a) an n-ary convexity is $4 iff every pair of disjoint polytopes with at most n vertices can be separated by complementary half spaces, and b) an interv...

For a function defined on a convex set in a Euclidean space, midpoint convexity is the property requiring that the value of the function at the midpoint of any line segment is not greater than the average of its values at the endpoints of the line segment. Midpoint convexity is a well-known characterization of ordinary convexity under very mild assumptions. For a function defined on the integer...

In this paper we study the relations between superadditivity and several types of convexity for cooperative games with random payoffs. The types of convexity considered are marginal convexity (all marginal vectors belong to the core), individual-merge convexity (any individual player is better off joining a larger coalition) and coalitional-merge convexity (any coalition of players is better of...

We consider a digital fuzzy set placed in Oxyplane, with support which is a set of digital points (centroids) in Z. We consider two kinds of convexity of a fuzzy set, namely quasi convexity and strong convexity, and we propose two algorithms for the construction of both kinds of convex hull of a digital fuzzy set.

In this paper we give generalization of Opial-type inequalities by using generalized fractional integral operator involving generalized Mittag–Leffler function. We deduce some results which already have been proved. Also we consider n -exponential convexity of some non-negative differences of inequalities involving Mittag-Leffler function and deduce their exponential convexity and log-convexity.

A new light is shed on “substitutes and complements” in the maximum weight circulation problem with reference to the concepts of L-convexity and M-convexity in the theory of discrete convex analysis. This provides us with a deeper understanding of the relationship between convexity and submodularity in combinatorial optimization.

In this article, we define a new class of convexity called generalized $(h-m)$-convexity, which generalizes $h$-convexity and $m$-convexity on fractal sets $\mathbb{R}^{\alpha}$ $(0<\alpha\leq 1)$. Some properties are discussed. Using local fractional integrals Hermite-Hadamard (H-H) Fej\'er-Hermite-Hadamard (Fej\'er-H-H) types inequalities. We also obtained result the Fej\'er-H-H type for func...