Abstract
The aim of this paper is to study a new family of measures of noncompactness in the space \({L^1_{\text{loc}}(\mathbb{R}_+)}\) consisting of all real functions locally integrable on \({\mathbb{R}_+}\) , equipped with a suitable topology. As an example of applications of the technique associated with that family of measures of noncompactness, we study the existence of solutions of a nonlinear Volterra integral equation in the space \({L^1_{\text{loc}}(\mathbb{R}_+)}\) . The obtained result generalizes several ones obtained earlier with help of other methods.
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Olszowy, L. A Family of Measures of Noncompactness in the Space \({L^1_{\text{loc}}(\mathbb{R}_+)}\) and its Application to Some Nonlinear Volterra Integral Equation. Mediterr. J. Math. 11, 687–701 (2014). https://doi.org/10.1007/s00009-013-0375-9
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DOI: https://doi.org/10.1007/s00009-013-0375-9