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Równania - test

Let $X$ be a Banach space without the Schur property. We say that $X$ is nearly uniformly noncreasy (NUNC for short) if for every $\epsilon>0$ there is $t>0$ such that for every $x\in S_{X}$ it is the case that $$d\left( \epsilon ,x\right) \geq t$$ or $$b\left( t,x\right) \leq \epsilon t.$$ Additionally, we treat spaces with the Schur property as being NUNC.