we introduce a new one-step iteration process to approximate common fixed points of twononexpansive mappings in banach spaces and prove weak convergence of the iterative sequence using (i)opial’s condition and (ii) kadec-klee property. strong convergence theorems are also established in banachspaces and uniformly convex banach spaces under the so-called condition ( a ), which is weaker thancom...

Berinde [V. Berinde, Approximating fixed points of weak contractions using the Picard iteration, Nonlinear Anal. Forum {bf 9} (2004), 43-53] introduced almost contraction mappings and proved Banach contraction principle for such mappings. The aim of this paper is to introduce the notion of multivalued almost $Theta$- contraction mappings andto prove some best proximity point results for t...

Stability of a power grid’s synchronous operating mode is crucial to its reliable function. We quantify the stability of this operating mode in different humble power grid layouts that we numerically simulate employing a widely used electro-mechanical model. The method with which we quantify stability delivers a single number, called basin stability, for each node in a grid. A node with a poor ...

In [13], Migliore–Miró-Roig–Nagel show that the Weak Lefschetz property can fail for an ideal I ⊆ K[x1, . . . , x4] generated by powers of linear forms. This is in contrast to the analogous situation in K[x1, x2, x3], where WLP always holds [16]. We use the inverse system dictionary to connect I to an ideal of fat points, and show that failure of WLP for powers of linear forms is connected to t...

A sufficient condition that the product of two compact spaces has the property of weak approximation by points (briefly WAP) is given. It follows that the product of the unit interval with a compact WAP space is also a WAP space.