On the class of relatively weakly demicompact nonlinear operators


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	On the class of relatively weakly demicompact nonlinear operators


	Fixed Point Theory, Volume 19, No. 2, 2018, 625-630, June 1st, 2018 DOI: 10.24193/fpt-ro.2018.2.49 Authors: Bilel Krichen and Donal O'Regan Abstract: In this paper we discuss some topological properties of the set $\mathcal{\mathcal{F}}(S_{0}, T, z):=\left\{x\in X: S_{0}x \in Tx + z\right\},$ where T is a nonlinear multi-valued mappings and S₀ is a single-valued mappings acting on a Banach space X. This study is based on a new concept, the so called weakly relative demicompactness for nonlinear operators. Key Words and Phrases: Demicompact operator, multi-valued mapping, weak topology, measure of weak noncompactness. 2010 Mathematics Subject Classification: 58C07, 47H04. Published on-line: June 1st, 2018. Abstract pdf Fulltext pdf Back to volume's table of contents