On mappings with diminishing orbital diameters

On mappings with diminishing orbital diameters

We introduce the concepts of ∗-diminishing orbital diameters and diminishing orbital diameters for a pair (f ,g) of self mappings in metric spaces and prove common fixed point theorems for these mappings. The results obtained in this paper extend properly the result of Fisher (1978). 2000 Mathematics Subject Classification. 54H25.

Fixed point theorems for mappings with convex diminishing diameters on cone metric spaces

On Identities with Additive Mappings in Rings

begin{abstract} If $F,D:Rto R$ are additive mappings which satisfy $F(x^{n}y^{n})=x^nF(y^{n})+y^nD(x^{n})$ for all $x,yin R$. Then, $F$ is a generalized left derivation with associated Jordan left derivation $D$ on $R$. Similar type of result has been done for the other identity forcing to generalized derivation and at last an example has given in support of the theorems. end{abstract}

Large Deviations with Diminishing Rates

The theory of large deviations for jump Markov processes has been generally proved only when jump rates are bounded below, away from zero (Dupuis and Ellis, 1995, The large deviations principle for a general class of queueing systems I. Trans. Amer. Math. Soc. 347 2689–2751; Ignatiouk-Robert, 2002, Sample path large deviations and convergence parameters. Ann. Appl. Probab. 11 1292–1329; Shwartz...

Large Deviations with Diminishing Rate

The theory of large deviations for jump Markov processes has been generally proved only when jump rates are bounded below, away from zero [4, 8, 12]. Yet various applications of interest do not satisfy this condition. We describe several classes of models where jump rates diminish to zero in a Lipschitz continuous way. Under appropriate conditions, we prove that the sample path large deviations...