We identify some classes $$\mathcal {C}$$ of mixed groups such that if $$G\in \mathcal has the cancellation property then Walk-endomorphism ring G unit lifting property. In particular, is a self-small group torsion-free rank at most 4 with it decomposition $$G=F\oplus H$$ F free and H

For positive semidefinite matrices A and B, Ando and Zhan proved the inequalities |||f(A) + f(B)||| ≥ |||f(A + B)||| and |||g(A) + g(B)||| ≤ |||g(A + B)|||, for any unitarily invariant norm, and for any non-negative operator monotone f on [0,∞) with inverse function g. These inequalities have very recently been generalised to non-negative concave functions f and non-negative convex functions g,...

In this paper we extend the notion of a Lorentz cone. We call a closed convex set isotone projection set with respect to a pointed closed convex cone if the projection onto the set is isotone (i.e., monotone) with respect to the order defined by the cone. We determine the isotone projection sets with respect to an extended Lorentz cone. In particular a Cartesian product between an Euclidean spa...

Given a graph property $\Phi$, the problem $\#\ensuremath{{\sc IndSub}}(\Phi)$ asks, on input of $G$ and positive integer $k$, to compute number $\#{\ensuremath{{IndSub}({\Phi,k} \to {G})}}$ induced subgraphs size $k$ in that satisfy $\Phi$. The search for explicit criteria $\Phi$ ensuring is hard was initiated by Jerrum Meeks [J. Comput. System Sci., 81 (2015), pp. 702--716] part major line re...

*Correspondence: [email protected] 2Department of Mathematics and Applied Mathematics, University of Pretoria, Lynwood Road, Pretoria, 002, South Africa Full list of author information is available at the end of the article Abstract In this paper, employing a new concept of generalized compatibility of a pair of mappings defined on a product space, certain coupled coincidence point results...

The subject is the overview of the use of quasi-entropy in finite dimensional spaces. Operator monotone functions and relative modular operators are used. The origin is the relative entropy, and the f -divergence, monotone metrics, covariance and the χ2-divergence are the most important particular cases. The extension of monotone metrics to those with two parameters is a new concept. Monotone m...

The purpose of this paper is to establish some coupled coincidence point theorems for a pair of mappings without mixed monotone property satisfying a contractive condition of rational type in the framework of partially ordered metric spaces. Also, we present a result on the existence and uniqueness of coupled common fixed points. The results presented in the paper generalize and extend several ...

This paper is concerned with a weakly coupled system of quasilinear parabolic equations where the coefficients are allowed to be discontinuous and the reaction functions may depend on continuous delays. By the method of upper and lower solutions and the associated monotone iterations and by difference ratios method and various estimates, we obtained the existence and uniqueness of the global pi...