In this paper we generalize the well known converse to the contraction principle due to C. Bessaga, dropping the uniqueness of the fixed point from its hypotheses. Some properties of weakly Picard mappings are given.

In this paper, we establish weak and strong convergence theorems for mean nonexpansive maps in Banach spaces under the Picard–Mann hybrid iteration process. We also construct an example of mappings show that it exceeds class mappings. To numerical accuracy our main outcome, process is more effective than all Picard, Mann, Ishikawa iterative processes.

We prove birational boundedness of Q-Fano varieties with Picard number one in arbitrary dimension.

We prove that the family of Q-Fano threefolds with Picard number one is birationally unbounded.

We prove birational boundedness of Q-Fano varieties with Picard number one in arbitrary dimension.

We prove birational boundedness of Q-Fano varieties with Picard number one in arbitrary dimension.

In this paper, we demonstrate via an example a variety of techniques both general and ad hoc that can be used to find the group of automorphisms of a K3 surface. Introduction Given a K3 surface X/k over a number field k, what is its group of automorphisms A = Aut(X/k)? In this paper, we offer some ideas of how to answer this natural question, and demonstrate these ideas by applying them to a pa...

Recently J.C. Rohde constructed families of Calabi-Yau threefolds parametrised by Shimura varieties. The points corresponding to threefolds with CM are dense in the Shimura variety and, moreover, the families do not have boundary points with maximal unipotent monodromy. Both aspects are of interest for Mirror Symmetry. In this paper we discuss one of Rohde’s examples in detail and we explicitly...