We consider the problem of minimizing a class of quasi-concave functions over a convex set. Quasiconcave functions are a generalization of concave functions and thus, NP-hard to minimize over a convex set in general. We present a simple fully polynomial time approximation scheme (FPTAS) for minimizing a fairly general class of low-rank quasi-concave functions. Our algorithm is based on solving ...

We provide a dual representation of quasi-convex maps π : LF → LG , between two locally convex lattices of random variables, in terms of conditional expectations. This generalizes the dual representation of quasi-convex real valued functions π : LF → R and the dual representation of conditional convex maps π : LF → LG . These results were inspired by the theory of dynamic measurements of risk a...

Motivated by the recent work on symmetric analytic functions using concept of Faber polynomials, this article introduces and studies two new subclasses bi-close-to-convex quasi-close-to-convex associated with Janowski functions. By polynomial expansion method, it determines general coefficient bounds for belonging to these classes. It also finds initial coefficients bi-quasi-convex Some known c...

In this paper, we introduce some new subclasses of analytic functions related to starlike, convex, close-to-convex and quasi-convex functions defined by using a generalized operator. Inclusion relationships for these subclasses are established. Also, we introduce some integral-preserving properties. Moreover, connections of the results presented here with those obtained in earlier works are poi...

In this paper we find a characterization type result for (η1,η2)-convex functions. The Fejér integral inequality related to (η1,η2)-convex functions is obtained as a generalization of Fejér inequality related to the preinvex and η-convex functions. Also some Fejér trapezoid and midpoint type inequalities are given in the case that the absolute value of the derivative of considered function is (...

The clustering problem as a problem of set function optimization with constraints is considered. The behavior of quasi-concave functions on antimatroids and on convex geometries is investigated. The duality of these two set function optimizations is proved. The greedy type Chain algorithm, which allows to find an optimal cluster, both as the “most distant” group on antimatroids and as a dense c...

Hermite-Hadamard inequality is one of the fundamental applications of convex functions in Theory of Inequality. In this paper, Hermite-Hadamard inequalities for $mathbb{B}$-convex and $mathbb{B}^{-1}$-convex functions are proven.

the aim of this paper is to prove some inequalities for p-valent meromorphic functions in thepunctured unit disk δ* and find important corollaries.