Fixed point theorems in KΛ-g.l.c.s. via ℳᴧ-measures of noncompactness
DOI:
https://doi.org/10.12775/TMNA.2025.049Keywords
Fixed point, cone normed space, measure of noncompactness, seminormAbstract
In this paper, we introduce a class of locally convex spaces $(X, \Lambda)$ endowed with a topology generated by a family $\Lambda$ of $K$-seminorms, along with a family of generalized non-compact measures $\mathcal{M}_\Lambda$ taking values in the corresponding family of ordered sets $(R_p, \preceq_p)_{p \in \Lambda}$. We establish several fixed point theorems for $Q$-$\Lambda$-g-Lipschitz operators, $\mathcal{M}_\Lambda$-g-condensing/contraction operators, and mappings defined as the sum of such operators. These results are applied to address the existence and uniqueness of nonlocal solutions to generalized integrodifferential equations. Through illustrative examples, the paper demonstrates the utility of the family of $K$-seminorms and the family of generalized non-compact measures $\mathcal{M}_\Lambda$ in studying the existence of fixed points.References
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