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Points of Upper and Lower Semicontinuity for Multivalued Functions

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Ukrainian Mathematical Journal Aims and scope

We investigate joint upper and lower semicontinuity of two-variable set-valued functions. More precisely, among other results, we show that, under certain conditions, a two-variable lower horizontally quasicontinuous mapping F : X × Y → K(Z) is jointly upper semicontinuous on sets of the form D × {y0}, where D is a dense G𝛿 -subset of X and y0 ∈ Y. A similar result was obtained for the joint lower semicontinuity of upper horizontally quasicontinuous mappings. These results improve some known results on the joint continuity of single-valued functions.

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Authors and Affiliations

  1. Ferdowsi University of Mashhad, Mashhad, Iran

    A. K. Mirmostafaee

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  1. A. K. Mirmostafaee
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 69, No. 9, pp. 1224–1231, September, 2017.

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Mirmostafaee, A.K. Points of Upper and Lower Semicontinuity for Multivalued Functions. Ukr Math J 69, 1424–1432 (2018). https://doi.org/10.1007/s11253-018-1441-z

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  • DOI: https://doi.org/10.1007/s11253-018-1441-z

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