Some fixed point theorems for set valued directional contraction mappings

V. M. Sehgal

International Journal of Mathematics and Mathematical Sciences, 1980, vol. 3, 1-6

Abstract:

Let S be a subset of a metric space X and let B ( X ) be the class of all nonempty bounded subsets of X with the Hausdorff pseudometric H . A mapping F : S → B ( X ) is a directional contraction iff there exists a real α ∈ [ 0 , 1 ) such that for each x ∈ S and y ∈ F ( x ) , H ( F ( x ) , F ( z ) ) ≤ α d ( x , z ) for each z ∈ [ x , y ] ∩ S , where [ x , y ] = { z ∈ X : d ( x , z ) + d ( z , y ) = d ( x , y ) } . In this paper, sufficient conditions are given under which such mappings have a fixed point.

Date: 1980
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:390981

DOI: 10.1155/S0161171280000336

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