In this paper, we generalize and investigate the Bohr-Rogosinski inequalities property for subfamilies of univalent functions defined on unit disk D:={z∈C:|z|<1} which maps to concave domain, i.e., domain whose complement is a convex set. All results are proved be sharp.

Many combinatorial optimization problems can be formulated as: for a given set system over E (i.e., for a pair (E, ) where ⊆ 2E is a family of feasible subsets of finite set E), and for a given function F : →R, find an element of for which the value of the function F is minimum or maximum. In general, this optimization problem is NP-hard, but for some specific functions and set systems the prob...

Perception based function (PBF) is given by the set of rules Ri:“If X is Ti then Y is Si”, where Ti is a linguistic term describing some fuzzy intervals Ai on the domain of real values of X and Si is a linguistic description of the shape of the function Y(X) on this interval. The methods of explicitation of such type of rules when Si are given by words QUICKLY INCREASING AND SLIGHTLY CONVEX, SL...

Mixed f -divergences, a concept from information theory and statistics, measure the difference between multiple pairs of distributions. We introduce them for log concave functions and establish some of their properties. Among them are affine invariant vector entropy inequalities, like new Alexandrov-Fenchel type inequalities and an affine isoperimetric inequality for the vector form of the Kull...

In the authors introduced a technique which enabled them to solve the parametric minimum cycle problem with a xed number of parameters in strongly polynomial time In the current paper we present this technique as a general tool In order to allow for an independent reading of this paper we repeat some of the de nitions and propositions given in Some proofs are not repeated however and instead we...