On coincidence points for a Zamfirescu type pair of multi-valued mappings

A concept of a pair of multi-valued Zamfirescu type mappings between metric spaces is introduced. A coincidence existence theorem is proved for such pairs of mappings. It is shown that the obtained result is a generalization of the main result of the recent joint work by the authors Kritsana Neammanee and Annop Kaevkhao, in which the concept of a multi-valued Zamfirescu mapping was introduced and the fixed point existence and approximation theorem was proved. In addition, it is shown in this paper that all listed results are partial cases of the search principle for zeros of special $(1,\lambda)$-search functionals proposed earlier by T. N. Fomenko.