Abstract measures of noncompactness and fixed points for nonlinear mappings



	Abstract measures of noncompactness and fixed points for nonlinear mappings


	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. Abstract pdf Fulltext pdf Back to volume's table of contents