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.

in this paper we study properties of symbols such that these belong to class of symbols sitting insidesm ρ,φ that we shall introduce as the following. so for because hypoelliptic pseudodifferential operatorsplays a key role in quantum mechanics we will investigate some properties of m−hypoelliptic pseudodifferential operators for which define base on this class of symbols. also we consider maxi...

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...