A multivalued version of Krasnoselskii’s theorem in generalized Banach spaces
| Oct 20, 2015
Published Online: Oct 20, 2015
Page range: 177 - 192
Received: Aug 01, 2012
Accepted: Feb 01, 2013
DOI: https://doi.org/10.2478/auom-2014-0041
Keywords
Compact operator, fixed point, generalized contraction, generalized Banach space, generalized metric space, integral inclusions system, iterative method, Krasnoselskii’s theorem, -contraction, matrix convergent to zero, multivalued operator, Perov’s theorem, relatively compact operator, sum of two operators, vector-valued metric, vector-valued norm, Fredholm-Volterra type inclusions system
© 2014 Ioan-Radu Petre, published by De Gruyter Open
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.
The purpose of this paper is to extend Krasnoselskii’s fixed point theorem to the case of generalized Banach spaces for multivalued operators. As application, we will give an existence result for a system of Fredholm-Volterra type differential inclusions.