An operator (A: P rightarrow P) is said to be sub-homogeneous if it satisfies A(tx) geq tA x), quadforall t in 0,1), xin P. (2.1).
An operator (A: Erightarrow E) is said to be positive homogeneous if it satisfies (A(tx)=tAx), (forall t>0), (xin E).
An operator (A: Prightarrow P) is said to be sub-homogeneous if it satisfies A(tx geq tAx, quad forall tin 0,1), xin P. ([30]).
An operator (A: Prightarrow P) is said to be r-concave if it satisfies A(tx geq t^{r}Ax, quad forall tin 0, 1), xin P. ([31]).
An operator (A Drightarrow D) is said to be α-concave if it satisfies A(tx geq t^{alpha}Ax, quad forall tin 0,1),xin D. (2.13).
An operator (A: Prightarrow P) is said to be r-concave if it satisfies A(tx geq t^{r}Ax, quad forall tin 0, 1), xin D. (11).
An operator (A: D rightarrow D) is said to be β-concave if it satisfies A(tx) geq t^{beta}A x), quadforall t in 0,1), xin D. (2.2).
An operator (A: P rightarrow P) is said to be sub-homogeneous if it satisfies A(tx) geq tA x), quadforall t in 0,1), xin P. Let α be a real number with (0leqalpha < 1).
I'm impressed by Tate Modern and its vast Turbine Hall, with its echoes of Albert Speer and the Zeppelin field rallies, and its immense popularity proves that it satisfies a need that should have been met by the disastrous Millennium Dome, a wish for an uplifting social space more enduring than the local Tesco or Ikea.
It satisfies a number of criteria indicating its suitability as a measure of dependence[ 29].
"It satisfies a neo-liberal nostalgia for community and spirituality.
