Author(s): Lj B CIRIC
Let T: M —> M be a mapping of a metric space (M, d) into itself. A mapping T will be called a quasi-contraction iff d(Tx, Ty) s q • max\d(x, y); d(x, Tx); d(y, Ty); d(x, Ty); d(y, Tx)\ for some q < 1 and all x, y e M. In the present paper the mappings of this kind are investi- gated. The results presented here show that the condition of quasi-con- tractivity implies all conclusions of Banach's contraction principle. Multi-valued quasi-contractions are also discussed.