In this paper, we will show that under certain circumstances, a two variable set-valued mapping F:X×Y→2Zis jointly continuous on a set of the form D×{y}, where Dis a dense Gδsubset of Xand y∈Y. Among some other results, we will show that if Xis a Baire space, Ya topological space and Zis a Tychonoff locally weakly k-developable space, then every set-valued mapping Ffrom X×Yinto compact subsets of Z, is Vietoris continuous at each point of X×{y0}, where y0∈Yis a W-point, provided that all its x-sections Fxare Vietoris continuous and all its y-sections Fyare Vietoris quasi-continuous. Our results improve some old related results in the literature Our results improve some old related results in the literature.

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