Restricted-orientation convexity, also called O-convexity, is the study of geometric objects whose intersection with lines from some fixed set is empty or connected. We introduce restricted-orientation halfspaces, which are an O-convexity analog of halfspaces, explore their properties, and demonstrate their relationship to restricted-orientation convex sets.

In [K.-I. Mitani and K.-S. Saito, J. Math. Anal. Appl. 327 (2007), 898–907] we characterized the strict convexity, uniform convexity and uniform non-squareness of Banach spaces using ψ-direct sums of two Banach spaces, where ψ is a continuous convex function with some appropriate conditions on [0, 1]. In this paper, we characterize the Bn-convexity and Jn-convexity of Banach spaces using ψ-dire...

It is well known that subsets of the two-dimensional space ¢ 2 can represent prominent musical and music-theoretical objects such as scales, chords and chord vocabularies. It has been noted that the major and minor diatonic scale form convex subsets in this space. This triggers the question whether convexity is a more widespread concept in music. This article systematically investigates the con...

Convexity represents a fundamental descriptor of object shape. This paper presents a new convexity measure for both open and closed simple contours. Given such a contour this measure extracts two corresponding open convex hulls. The shape similarity between these two hulls and the original contour is then computed and normalized to give a measure of convexity. The time complexity of the propose...

Based on the original geometrical definition of the planar parametric convex curve, the local convexity and the global convexity on parametric curve are discussed, a few properties are obtained, and a necessary and sufficient condition is presented for the local convexity of a general planar parametric curve.

The monotonicity and the Schur-convexity with parameters (s, t) in R2 for fixed (x, y) and the Schur-convexity and the Schur-geometrically convexity with variables (x, y) in R++ for fixed (s, t) of Gini mean G(r, s;x, y) are discussed. Some new inequalities are obtained.

We treat the classical notion of convexity in the context of hard real analysis. Definitions of the concept are given in terms of defining functions and quadratic forms, and characterizations are provided of different concrete notions of convexity. This analytic notion of convexity is related to more classical geometric ideas. Applications are given both to analysis and geometry.

In this paper, we provide an alternative definition of NTU convexity, strongly ordinal convexity. We show that if a game is strongly ordinal convex, then any marginal worth vector is in the core, and any marginal contribution is increasing. Some economic examples satisfy this convexity. KeywordsCooperative game; Convex game; NTU game; Core; Supermodularity JEL classification codes: C62; D52; D53