Fixed point theorems for upper semicontinuous multivalued operators in locally convex spaces

Bilel Krichen; Fatima Bahidi;


In the present paper, we will discus some $\tau$-topological properties of the set $\mathcal{\mathcal{F}}(S_{0}, T, H):=\left\{ x\in X: S_{0}x \in Tx + Hx \right\}$, where $ T $ is multivalued operator, $S_{0}$ and $H$ are two single valued operators acting on a Hausdorff locally convex space $X $ and $\tau$ is a weaker Hausdorff locally convex topology on $X$. Moreover, when $X$ is a $\tau$-angelic space with the so-called $\tau$-Krein-\v{S}mulian property, we will provide some new variants of fixed point theorems for multivalued operators. Our results are formulated in terms of $\tau$-upper semicontinuity, $\tau$-$S_{0}$-demicompactness and families of axiomatic measures of noncompactenss.

Vol. 24 (2023), No. 1, pp. 235-246

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