Fixed point theorem of generalized quasi-contractive mapping in cone metric space. (English) Zbl 1231.65101
Summary: We introduce the generalized quasi-contractive mapping in a cone metric space . is called a generalized quasi-contractive if there is a real such that for all , for some . It is proved that if is a complete cone metric space with normal cone then has a unique fixed point. A example is given, which shows that our result is a genuine generalization of quasi-contractive mapping.
|65J15||Equations with nonlinear operators (numerical methods)|
|47H10||Fixed point theorems for nonlinear operators on topological linear spaces|
|47H09||Mappings defined by “shrinking” properties|