Some Properties of Generalized Higher-order Convexity
نویسنده
چکیده
The generalized divided differences are introduced. They are applied to investigate some properties characterizing generalized higher-order convexity. Among others some support-type property is proved.
منابع مشابه
Higher-order symmetric duality for a class of multiobjective fractional programming problems
Correspondence: gaoyingimu@163. com Department of Mathematics, Chongqing Normal University, Chongqing 400047, China Abstract In this paper, a pair of nondifferentiable multiobjective fractional programming problems is formulated. For a differentiable function, we introduce the definition of higher-order (F, a, r, d)-convexity, which extends some kinds of generalized convexity, such as second or...
متن کاملLog-Convexity Properties of Schur Functions and Generalized Hypergeometric Functions of Matrix Argument
We establish a positivity property for the difference of products of certain Schur functions, sλ(x), where λ varies over a fundamental Weyl chamber in R n and x belongs to the positive orthant in R. Further, we generalize that result to the difference of certain products of arbitrary numbers of Schur functions. We also derive a log-convexity property of the generalized hypergeometric functions ...
متن کاملConvexity and Geodesic Metric Spaces
In this paper, we first present a preliminary study on metric segments and geodesics in metric spaces. Then we recall the concept of d-convexity of sets and functions in the sense of Menger and study some properties of d-convex sets and d-convex functions as well as extreme points and faces of d-convex sets in normed spaces. Finally we study the continuity of d-convex functions in geodesic metr...
متن کاملSOME PROPERTIES FOR FUZZY CHANCE CONSTRAINED PROGRAMMING
Convexity theory and duality theory are important issues in math- ematical programming. Within the framework of credibility theory, this paper rst introduces the concept of convex fuzzy variables and some basic criteria. Furthermore, a convexity theorem for fuzzy chance constrained programming is proved by adding some convexity conditions on the objective and constraint functions. Finally,...
متن کاملSome results on pre-monotone operators
In this paper, some properties of pre-monotone operators are proved. It is shown that in a reflexive Banach space, a full domain multivalued $sigma$-monotone operator with sequentially norm$times$weak$^*$ closed graph is norm$times$weak$^*$ upper semicontinuous. The notion of $sigma$-convexity is introduced and the relations between the $sigma$-monotonicity and $sigma$-convexity is i...
متن کامل