This note investigates the convexity of the indefinite joint numerical range of a tuple of Hermitian matrices in the setting of Krein spaces. Its main result is a necessary and sufficient condition for convexity of this set. A new notion of “quasi-convexity” is introduced as a refinement of pseudo-convexity.

This paper investigates the stochastic linear quadratic (LQ, for short) optimal control problem of Markovian regime switching system. The representation cost functional LQ system is derived by technique Itô’s formula with jumps. For system, we establish equivalence between open-loop (closed-loop, resp.) solvability and existence an adapted solution to corresponding forward-backward differential...

In this paper, acceleration of gradient methods for convex optimization problems with weak levels convexity and smoothness is considered. Starting from the universal fast method which was designed to be an optimal weakly smooth whose gradients are Hölder continuous, its momentum modified appropriately so that it can also accommodate uniformly problems. Different existing works, proposed in pape...

In this paper, we introduce a new convexity on graphs similar to the well known P3convexity [3], which we will call P ∗ 3 -convexity. We show that several P ∗ 3 -convexity parameters (hull number, convexity number, Carathéodory number, Radon number, interval number and percolation time) are NP-hard even on bipartite graphs. We show a strong relation between this convexity and the well known geo...

In this paper, the Schur convexity is generalized to Schur f -convexity, which contains the Schur geometrical convexity, harmonic convexity and so on. When f : R+ →R is defined by f (x) = (xm−1)/m if m = 0 and f (x) = lnx if m = 0 , the necessary and sufficient conditions for f -convexity (is called Schur m -power convexity) of Daróczy means are given, which improve, generalize and unify Shi et...

the object of this paper to derive certain sucient condi-tions for close-to-convexity of certain analytic functions dened on theunit disk

We consider the long time behavior of heterogeneously interacting diffusive particle systems and their large population limit. The interaction is mean field type with weights characterized by an underlying graphon. limit given a graphon system consisting independent but heterogeneous nonlinear diffusions whose probability distributions are fully coupled. Under suitable assumptions, including ce...

Inthis paper, the main aim is to introduce the class $mathcal{U}_p(lambda,alpha,beta,k_0)$ of $p$-harmonic mappings togetherwith its subclasses $mathcal{U}_p(lambda,alpha,beta,k_0)capmathcal {T}_p$ and $mathcal{U}_p(lambda,alpha,beta,k_0)capmathcal {T}_p^0$, andinvestigate the properties of the mappings in these classes. First,we give a sufficient condition for mappings to be in $mathcal{U}_p(l...