A pointwise contraction criteria for the existence of fixed points

V. M. Sehgal

International Journal of Mathematics and Mathematical Sciences, 1979, vol. 2, 1-8

Abstract:

Let S be a subset of a metric space ( X , d ) and T : S → X be a mapping. In this paper, we define the notion of lower directional increment Q T ( x , y ] of T at x ∈ S in the direction of y ∈ X and give sufficient conditions for T to have a fixed point when Q T ( x , T x ] < 1 for each x ∈ S . The results herein generalize the recent theorems of Clarke (Caned. Math. Bull. Vol. 21(1), 1978, 7-11) and also improve considerably some earlier results.

Date: 1979
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:718790

DOI: 10.1155/S0161171279000363

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