Measures of noncompactness related to monotonicity

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EXISTENCE AND ASYMPTOTIC STABILITY OF SOLUTIONS OF A PERTURBED FRACTIONAL FUNCTIONAL-INTEGRAL EQUATION WITH LINEAR MODIFICATION OF THE ARGUMENT (2011, methodology): “Now, we recollect the construction of the measure of noncompactness in BC(R+) which will be used in the next section (see [7]).”
Measure of Noncompactness and Fractional Differential Equations in Frechet Spaces (2020, unknown): “[6, 7, 8, 9, 10, 11], El-Sayed and Rzepka [18], Guo et al.”
On a Class of Measures of Noncompactness in Banach Algebras and Their Application to Nonlinear Integral Equations (2009, unknown): “[7]): d(x) = sup{|x(s) − x(t)| − [x(s) − x(t)] : t, s ∈ [a, b], t ≤ s} i(x) = sup{|x(s) − x(t)| − [x(t) − x(s)] : t, s ∈ [a, b], t ≤ s} .”