We prove that any bounded linear operator on Lp[0, 1] for 1 6 p < ∞, commuting with the Volterra operator V , is not weakly supercyclic, which answers affirmatively a question raised by Léon-Saavedra and Piqueras-Lerena. It is achieved by providing an algebraic flavored condition on an operator which prevents it from being weakly supercyclic and is satisfied for any operator commuting with V . ...

We discuss about the generalized $F$-contraction mappings in partially ordered metric spaces. For this, we first introduce the notion of ordered weakly $F$-contraction mapping. We also present some fixed point results about this type of mapping in partially ordered metric spaces. Next, we introduce the notion of $acute{mathrm{C}}$iri$acute{mathrm{c}}$ type generalized ordered weakly $F$-contrac...

We discuss the canonical structure of a class of integrable quantum mappings, i.e. iterative canonical transformations that can be interpreted as a discrete dynamical system. As particular examples we consider quantum map-pings associated with the lattice analogues of the KdV and MKdV equations. These mappings possess a non-ultralocal quantum Yang-Baxter structure leading to the existence of co...

This paper is devoted to prove the S. L. Singh’s common fixed point Theorem for commuting mappings in cone metric spaces. In this framework, we introduce the notions of generalized Kannan contraction, generalized Zamfirescu contraction and generalized Weak contraction for a pair of mappings, proving afterward fixed point results.

In this paper, we continue the study of contractive conditions for mappings in complete partial metric spaces. Concretely, we present fixed point results for weakly contractive and weakly Kannan mappings in such a way that the classical metric counterpart results are retrieved as a particular case. Special attention to the cyclical case is paid. Moreover, the well-posedness of the fixed point p...

In this paper a general fixed point theorem for converse commuting multivalued mappings, which generalize Theorems 2.1 and 2.2 from [3], is proved.

Let $n &amp;gt; 1 $ be a fixed positive integer and $S$ subset of ring $R$. A mapping $\zeta$ $R$ into itself is called $n$-skew-commuting on if $\zeta(x)x^{n} + x^{n}\zeta(x)=0$, $\forall$ $x\in S.$ The main aim this paper to describe mappings appropriate subsets With this, many known results can either generalized or deduced. In particular, solves the conjecture in [M. Nadeem, M. Aslam M.A. J...

In this paper, we introduce a new class of set-valued mappings which is called MD-type mappings. This class of mappings is a set-valued case of a class of the D-type mappings. The class of D-type mappings is a generalization of nonexpansive mappings that recently introduced by Kaewkhao and Sokhuma. The class of MD-type mappings includes upper semi-continuous Suzuki type mappings, upper semi-con...

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.