The EQ-5D health state utility values (HSUVs) at each time point are bounded from −0.54 to 1.00 where a score of less than zero is indicative of a health state worse than death.
The EQ-5D-3 L health state utility values (HSUVs) at each time point are bounded from −0.54 to 1.00 where a score of less than zero is indicative of a health state worse than death.
The EQ-5D HSUVs at each time point are bounded from -0.54 to 1.00 where a score of less than zero is indicative of a health state worse than death.
Therefore, we conclude that the operator T has at least one fixed point and the set of fixed points is bounded in Z. □.
Therefore, by Theorem 2.1, T has at least one fixed point and the set of fixed points is bounded in (Xtimes Y). □.
The Mandelbrot set M for the quadratic (Q_{c} z)=z^{2}+c) is defined as the collection of all (cin {C} ) for which the orbit of the point 0 is bounded, that is, M= bigl{ cin {C} : bigl{ Q_{c}^{n}(0) bigr} ;n=0,1,2,ldots bigr} is bounded.
If every firmly nonexpansive self-mapping on C has a fixed point, then C is bounded.
If every nonexpansive self-mapping on C has a fixed point, then C is bounded.
Therefore T has a unique fixed point since D is bounded; note that (T 0)=0).
Suppose that the sequence which generated by the hybrid proximal point Algorithm 3.5 is bounded, from Lemma 3.4, we have (3.24).
