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Compactness Criteria and Measures of Noncompactness in Function Spaces
Journal of the London Mathematical Society, 2000According to a result due to R.S. Phillips, if \((T_s)\) is a net of compact operators converging strongly to the identity, then a bounded set \(A\) in a Banach space is relatively compact if and only if \((T_s)\) converges uniformly on \(A\) to the identity. The aim of this paper is twofold.
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On nullity and fullness of measures of noncompactness
SCIENTIA SINICA Mathematica, 2023Chen Xiaoling, Cheng Lixin, He Wuyi
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On a measure of noncompactness in the space of continuous functions
1991For a bounded subset \(X\) of \(C[0,1]\) define \[ \omega_ 0(X)=\lim_{h\to 0} \sup_{x\in X} \sup\{| x(t)-x(s)|:\;| t-s|\leq h;\;t,s\in [0,1]\} \] and \[ p(X)=\sup_{t_ 0\in[0,1]} \lim_{h\to 0} \sup_{x\in X} \sup\{| x(t)-x(t_ 0)|:\;| t-t_ 0|\leq h;\;t\in[0,1]\}.
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Existence of fixed points and measures of weak noncompactness
Nonlinear Analysis: Theory, Methods & Applications, 2009Jesus Garcia-Falset
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