* Correspondence: [email protected] Department of Natural Sciences, Hong Duc University, Thanh Hoa, Vietnam Abstract In this paper, we prove a fixed point theorem for generalized weak contractions satisfying rational expressions in partially ordered metric spaces. The result is a generalization of a recent result of Harjani et al. (Abstr. Appl. Anal, Vol.2010, 1-8, 2010). An example is also gi...

We introduce the notion of Hypergraph Weighted Model (HWM) that generically associates a tensor network to a hypergraph and then computes a value by tensor contractions directed by its hyperedges. A series r defined on a hypergraph family is said to be recognizable if there exists a HWM that computes it. This model generalizes the notion of rational series on strings and trees. We prove some pr...

We construct some positive entropy automorphisms of rational surfaces with no periodic curves. The in question, which we term tri-Coble surfaces, are blow-ups \begin{document}$ \mathbb P^2$\end{document} at 12 points have contractions down to three different Coble surfaces. arise as compositions ...

recently, choudhury and metiya [fixed points of weak contractions in cone metric spaces, nonlinear analysis 72 (2010) 1589-1593] proved some fixed point theorems for weak contractions in cone metric spaces. weak contractions are generalizations of the banach's contraction mapping, which have been studied by several authors. in this paper, we introduce the notion of $f$-weak contractions and als...