Core elements (a la Aubin) of a fuzzy game can be associated with additive separable supporting functions of fuzzy games. Generalized cores whose elements consist of more general separable supporting functions of the game are introduced and studied. While the Aubin core of unanimity games can be empty, the generalized core of unanimity games is nonempty. Properties of the generalized cores and ...

This paper presents a framework for constructing and analyzing enclosures of the reachable set of nonlinear ordinary differential equations (ODEs) using continuous-time setpropagation methods. The focus is on convex enclosures that can be characterized in terms of their support functions. A generalized differential inequality is introduced, whose solutions describe such support functions for a ...

Any finite, separately convex, positively homogeneous function on R is convex. This was first established in [1]. In this paper, we give a new and concise proof of this result, and we show that it fails in higher dimension. The key of the new proof is the notion of perspective of a convex function f , namely, the function (x, y) → yf(x/y), y > 0. In recent works [9, 10, 11], the perspective has...

Some generalized Ostrowski-type integral inequalities for r−times differentiable functions whose absolute values are MT−convex have been discussed. Moreover, some applications on special bivariate means obtained.

In this manuscript, a new class of extended (m1,m2)-convex and concave functions is introduced. After some properties of (m1,m2)-convex functions have been given, the inequalities obtained with Hölder and Hölder-İşcan and power-mean and improwed power-mean integral inequalities have been compared and it has been shown that the inequality with Hölder-İşcan inequality gives a better approach than...

In this paper, we define the almost uniform convergence and the almost everywhere convergence for cone-valued functions with respect to an operator valued measure. We prove the Egoroff theorem for Pvalued functions and operator valued measure θ : R → L(P, Q), where R is a σ-ring of subsets of X≠ ∅, (P, V) is a quasi-full locally convex cone and (Q, W) is a locally ...

“Discrete Convex Analysis” is aimed at establishing a novel theoretical framework for solvable discrete optimization problems by means of a combination of the ideas in continuous optimization and combinatorial optimization. The theoretical framework of convex analysis is adapted to discrete settings and the mathematical results in matroid/submodular function theory are generalized. Viewed from ...