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Solving existence problems via $ F$-contractions


Author: Dariusz Wardowski
Journal: Proc. Amer. Math. Soc. 146 (2018), 1585-1598
MSC (2010): Primary 47H10, 47H09, 47H08, 47N20
DOI: https://doi.org/10.1090/proc/13808
Published electronically: December 28, 2017
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Abstract: The main results of the paper concern the existence of fixed points of nonlinear $ F$-contraction and the sum of this type of mapping with a compact operator. The results of Krasnosel'skii type are obtained with a usage of the Hausdorff measure of noncompactness and condensing mappings. The presented new tools give the possibility to verify the existence problems of the solutions for some classes of integral equations.


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Additional Information

Dariusz Wardowski
Affiliation: Department of Nonlinear Analysis, Faculty of Mathematics and Computer Science, University of Łódź, Banacha 22, 90-238 Łódź, Poland
Email: wardd@math.uni.lodz.pl

DOI: https://doi.org/10.1090/proc/13808
Keywords: Fixed point, nonlinear $F$-contraction, compact operator, condensing mapping, integral equation
Received by editor(s): February 2, 2017
Received by editor(s) in revised form: May 4, 2017
Published electronically: December 28, 2017
Communicated by: Wenxian Shen
Article copyright: © Copyright 2017 American Mathematical Society

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