Coincidence preservation for a one-parameter family of pairs of Zamfirescu-type multi-valued mappings (Q1980439)

A theorem is proved on the preservation of the existence of coincidence points in a given open subset of a metric space for a one-parameter family of pairs of Zamfirescu-type multi-valued mappings. The connection is demonstrated of this result with the Frigon-Granas theorem [\textit{M. Frigon} and \textit{A. Granas}, Topol. Methods Nonlinear Anal. 4, No. 1, 197--208 (1994; Zbl 0829.47047)] on the preservation of the existence of fixed points for a contraction family of multi-valued mappings.