Stability of coincidence points and set-valued covering maps in metric spaces

A study was conducted to demonstrate stability of coincidence points and set-valued covering maps in metric spaces. A set-valued map ψfrom X to Y was defined as a map sending each point x ε X to a non-empty closed subset ψ(x) of Y. The metric was defined in the Cartesian product X × Y by the formula φ = φx + φy. The set was called the graph of ψ and was denoted by gph(ψ), while a map was considered closed when its graph was closed. ψ was called a covering map when α > 0 existed for which ψ was an α-covering map. A set-valued map was also considered to be β-Lipschitz when it satisfied the Lipschitz condition with respect to the Hausdorff metric h with the constant β.