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A Family of Measures of Noncompactness in the Space $${L^1_{\text{loc}}(\mathbb{R}_+)}$$ and its Application to Some Nonlinear Volterra Integral Equation.
- Source :
- Mediterranean Journal of Mathematics; May2014, Vol. 11 Issue 2, p687-701, 15p
- Publication Year :
- 2014
-
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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 16605446
- Volume :
- 11
- Issue :
- 2
- Database :
- Complementary Index
- Journal :
- Mediterranean Journal of Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 95799134
- Full Text :
- https://doi.org/10.1007/s00009-013-0375-9