Fundamental Questions and New Counterexamples for b -Metric Spaces and Fatou Property

Ning Lu, Fei He and Wei-Shih Du
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Ning Lu: School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China
Fei He: School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China
Wei-Shih Du: Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 82444, Taiwan

Mathematics, 2019, vol. 7, issue 11, 1-15

Abstract: In this paper, we give new examples to show that the continuity actually strictly stronger than the Fatou property in b -metric spaces. We establish a new fixed point theorem for new essential and fundamental sufficient conditions such that a ?iri? type contraction with contraction constant λ ∈ [ 1 s , 1 ) in a complete b -metric space with s > 1 have a unique fixed point. Many new examples illustrating our results are also given. Our new results extend and improve many recent results and they are completely original and quite different from the well known results on the topic in the literature.

Keywords: b-metric space; Fatou property; ?iri? fixed point theorem; Banach contraction principle; Kannan’s fixed point theorem; Chatterjea’s fixed point theorem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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