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Fixed point results for generalized quasicontraction mappings in abstract metric spaces. (English) Zbl 1189.54036

Summary: We introduce the concept of generalized quasicontraction mappings in an abstract metric space. By using this concept, we construct an iterative process which converges to a unique fixed point of these mappings. The result presented in this paper generalizes the Banach contraction principle in the setting of metric space and a recent result of L.-G.Huang and X.Zhang [ibid.332, No.2, 1468–1476 (2007; Zbl 1118.54022)] for contractions. We also validate our main result by an example.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54F05 Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces
47H10 Fixed-point theorems
54E35 Metric spaces, metrizability

Citations:

Zbl 1118.54022
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References:

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