Some results on joint continuity of two variable set-valued mappings

In this paper, we will show that under certain circumstances, a two variable set valued mapping F : X x Y 2Z is jointly continuous on a set of the form D x {y}, where D is a dense G delta subset of X and y E Y. Among some other results, we will show that if X is a Baire space, Y a topological space and Z is a Tychonoff locally weakly k -developable space, then every set-valued mapping F from X x Y into compact subsets of Z, is Vietoris continuous at each point of X x {y0}, where y0 E Y is a W -point, provided that all its x -sections Fx are Vietoris continuous and all its y -sections Fy are Vietoris quasi-continuous. Our results improve some old related results in the literature. (c) 2023 Published by Elsevier B.V.