<span style="color: #333333; font-family: Calibri, sans-serif; font-size: 13.3333px; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: justify; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: #ffffff; text-dec...

We consider two different notions of convexity of metric spaces, namely (strict/uniform) ball convexity and (strict/uniform) distance convexity. Our main theorem states that (strict/uniform) distance convexity is preserved under a fairly general product construction, whereas we provide an example which shows that the same does not hold for (strict/uniform) ball convexity, not even when consider...

The approximate subdiierential introduced by Mordukhovich has attracted much attention in recent works on nonsmooth optimization. Potential advantages over other concepts of subdiierentiability might be related to its non-convexity. This motivates to study some topological properties more in detail. As the main result, it is shown that in a Hilbert space setting each weakly compact set may be o...

Problem of defining convexity of a digital region is considered. Definition of DL− (digital line) convexity is proposed, and it is shown to be stronger than the other two definitions, T−(triangle) convexity and L−(line) convexity. In attempt to connect the convexity of digital sets, to the fact that digital set can be a fuzzy set, the notion of convexity of the membership function is introduced...

Abstract In this paper, a complete picture of the different plastic failure modes that can be predicted by strain gradient plasticity model proposed in Del Piero et al. (J. Mech. Mater. Struct. 8:109–151, 2013) is drawn. The evolution problem elasto-plastic formulated as an incremental minimization acting on energy functional which includes local term and non-local contribution. Here, approxima...

In this paper we extend the result of [6] on the characteristic of convexity of Orlicz spaces to the more general case of Musielak-Orlicz spaces over a non-atomic measure space. Namely, the characteristic of convexity of these spaces is computed whenever the Musielak-Orlicz functions are strictly convex.

This note investigates the convexity of the indefinite joint numerical range of a tuple of Hermitian matrices in the setting of Krein spaces. Its main result is a necessary and sufficient condition for convexity of this set. A new notion of “quasi-convexity” is introduced as a refinement of pseudo-convexity.

A new stochastic approach for the approximation of (nonlinear) Lipschitz operators in normed spaces by their eigenvectors is shown. Different ways providing integral representations these approximations are proposed, depending on properties themselves whether they locally constant, (almost) linear, or convex. We use recently introduced notion eigenmeasure and focus attention procedures extendin...