# The behaviour of measures of noncompactness in $$L^\infty ({\mathbb {R}}^n)$$ L ∞ ( R n ) with application to the solvability of functional integral equations

The behaviour of measures of noncompactness in $$L^\infty ({\mathbb {R}}^n)$$ L ∞ ( R... In this work, we define a new measure of noncompactness on the space $$L^\infty ({\mathbb {R}}^n)$$ L ∞ ( R n ) . In addition, we study the existence of solutions for a class of nonlinear functional integral equations of Fredholm type by using an extension of Darbo’s fixed point theorem associated with this new measure of noncompactness. Also, we will include an example which shows the efficiency of our results. The obtained results improve several ones obtained earlier. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Springer Journals

# The behaviour of measures of noncompactness in $$L^\infty ({\mathbb {R}}^n)$$ L ∞ ( R n ) with application to the solvability of functional integral equations

, Volume 112 (2) – Apr 22, 2017
13 pages

/lp/springer_journal/the-behaviour-of-measures-of-noncompactness-in-l-infty-mathbb-r-n-l-r-CcvQhcsCVM
Publisher
Springer Milan
Subject
Mathematics; Mathematics, general; Applications of Mathematics; Theoretical, Mathematical and Computational Physics
ISSN
1578-7303
eISSN
1579-1505
D.O.I.
10.1007/s13398-017-0397-4
Publisher site
See Article on Publisher Site

### Abstract

In this work, we define a new measure of noncompactness on the space $$L^\infty ({\mathbb {R}}^n)$$ L ∞ ( R n ) . In addition, we study the existence of solutions for a class of nonlinear functional integral equations of Fredholm type by using an extension of Darbo’s fixed point theorem associated with this new measure of noncompactness. Also, we will include an example which shows the efficiency of our results. The obtained results improve several ones obtained earlier.

### Journal

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. MatemáticasSpringer Journals

Published: Apr 22, 2017

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