The minimax theorem for a convex-concave bifunction is a fundamental theorem in optimization and convex analysis, and has a lot of applications in economics. In the last two decades, a nonconvex extension of this minimax theorem has been well studied under various generalized convexity assumptions. In this note, by exploiting the hidden convexity (joint range convexity) of separable homogeneous...

This paper considers the generalized Stirling numbers of the first and second kinds. First, we show that the sequences of the above generalized Stirling numbers are both log-concave under some mild conditions. Then, we show that some polynomials related to the above generalized Stirling numbers are q-log-concave or q-log-convex under suitable conditions. We further discuss the log-convexity of ...

In this paper, we study some properties of quasiconvex nonlinear complementarity functions. However, we prove that a nonlinear complementarity function cannot be pseudoconvex. As a consequence of this, we show that every convex nonlinear complementarity function is nondifferentiable. Furthermore, some properties of homogeneous nonlinear complementarity functions are proved.

Abstract We introduce the subclass Tj(n, m, γ, α, λ) of analytic functions with negative coefficients defined by generalized Sălăgean operator D λ . Coefficient estimates, some important properties of the class Tj(n, m, γ, α, λ) and distortion theorems are determined. Further, extremal properties and radii of close-to-convexity, starlikeness and convexity of the class Tj(n, m, γ, α, λ) are obta...

For data satisfying certain generalized convexity conditions, the existence and uniqueness of a piecewise quadratic curvature continuous parametric spline interpolant in IR 2 is proved. Convexity is preserved by the interpolation, and the numerical construction of the interpolant can be carried out eeciently. The interpolation is 4{th order accurate, and a number of examples shows both the appl...

Abstract The main aim of this article is to present some novel geometric properties for three distinct normalizations the generalized k k -Bessel functions, such as radii uniform convexity and α \alpha -convexity. In addition, we show that -convexity remain in between starlikeness convexity, case when <m:m...

⎯The convexity assumptions for a minimax fractional programming problem of variational type are relaxed to those of a type I and related functions. Sufficient optimality conditions are established under the aforesaid assumptions. Several duality theorems are obtained for Wolfe type and Mond-Weir type duals and the original problem. Keyword⎯Minimax programming; Fractional programming; Sufficient...

Making use of the generalized Srivastava-Attiya integral operator, we define a new subclass of starlike functions with negative coefficients and obtain coefficient estimates, extreme points, the radii of close to convexity, starlikeness and convexity and neighbourhood results for f ∈ TS b (α, β, γ, A,B). In particular, we obtain modified Hadamard product results for the function f(z) belongs to...

We first present some basic properties of O-halfspaces and compare them with the properties of standard halfspaces. We show that O-halfspaces may be disconnected, characterize an Ohalfspace in terms of its connected components, and derive the upper bound on the number of components. We then study properties of the boundaries of O-halfspaces. Finally, we describe the complements of O-halfspaces ...

We consider linearly independent families of Hermitian matrices {A1, . . . , Am} so thatWk(A) is convex. It is shown that m can reach the upper bound 2k(n− k) + 1. A key idea in our study is relating the convexity of Wk(A) to the problem of constructing rank k orthogonal projections under linear constraints determined by A. The techniques are extended to study the convexity of other generalized...