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Fixed point theorem of generalized quasi-contractive mapping in cone metric space. (English) Zbl 1231.65101
Summary: We introduce the generalized quasi-contractive mapping f in a cone metric space (X,d). f is called a generalized quasi-contractive if there is a real λ[0,1) such that for all x,yX, d(fx,fy)λs for some sco{0,d(fx,fy),d(x,y),d(x,fx),d(y,fy),d(x,fy),d(y,fx)}. It is proved that if X is a complete cone metric space with normal cone then f has a unique fixed point. A example is given, which shows that our result is a genuine generalization of quasi-contractive mapping.
MSC:
65J15Equations with nonlinear operators (numerical methods)
47H10Fixed point theorems for nonlinear operators on topological linear spaces
47H09Mappings defined by “shrinking” properties
References:
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