Vol. 21(2020) No. 1

 

 

  Abstract measures of noncompactness and fixed points for nonlinear mappings
 
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Fixed Point Theory, Volume 21, No. 1, 2020, 47-66, February 1st, 2020

DOI: 10.24193/fpt-ro.2020.1.04

Authors: David Ariza-Ruiz and Jesús Garcia-Falset

Abstract: In this paper, we study the existence of fixed points for a mapping by using abstract measures of noncompactness. Thus, we can obtain some generalizations of Darbo and Sadovskiĭ's theorems and we also give a characterization for the existence of fixed points of a mapping which is not necessarily continuous. Finally, we solve an open problem proposed by I.A. Rus in 2001.

Key Words and Phrases: Measure of noncompactness, fixed points, continuous mappings.

2010 Mathematics Subject Classification: 47H09, 47H10, 47H30.

Published on-line: February 1st, 2020.

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