Fixed point results for multipoint Kannan-type mappings

We introduce and study a new type of mappings in metric spaces termed $n$-point Kannan-type mappings. A fixed-point theorem is proved for these mappings. In general case such mappings are discontinuous in the domain but necessarily continuous at fixed points. Conditions under which usual Kannan mappings and mapping contracting the total pairwise distances between $n$ points are $n$-point Kannan-type mappings are found. It is shown that additional conditions of asymptotic regularity and continuity allow to extend the value of the contraction coefficient in fixed-point theorems for $n$-point Kannan-type mappings.