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Some remarks on the generalized Banach contraction principle

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PL
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PL
This paper presents some results concerning the Generalized Banach Contraction Principle: In a complete metric space X if for some N ≥ 1 and 0 < M < 1 the mapping T : X → X satisfies min{d(Tj x,Tj y), 1 ≤ j ≤ N} ≤ Md(x, y) for any x, y ∈ X , then T has a unique fixed point. In some special cases, the above constant M can be replaced by a continuous, non- -increasing function 0 ≤ φ (d(x, y)) ≤ 1 such that φ (t) =1 if, and only if, t = 0.
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online
2016-02-17
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bwmeta1.element.ojs-nameId-6e3e8ea9-5a94-37a7-828b-e6cd5da23db6-year-2016-article-5734
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