Remarks on cyclic contractions in b-metric spaces and applications to integral equations

In this note we construct counterexamples to answer open questions on cyclic contractions posed by Radenović in (Afr Mat 27(1):291–295, 2016 ) and Radenović et al. (Appl Math Comput 273:155–164, 2016 ), and to show an error in the result of Nashine et al. (Publ Inst Math (Beograd) (N.S.) 93(107):69–...

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Bibliographic Details
Published in:Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas Físicas y Naturales. Serie A, Matemáticas, 2017, Vol.111 (1), p.247-255
Main Authors: Van Dung, Nguyen, Hang, Vo Thi Le
Format: Article
Language:English
Subjects:
Applications of Mathematics
Construction contracts
Errors
Integral equations
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Metric space
Original Paper
Theoretical
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Summary:In this note we construct counterexamples to answer open questions on cyclic contractions posed by Radenović in (Afr Mat 27(1):291–295, 2016 ) and Radenović et al. (Appl Math Comput 273:155–164, 2016 ), and to show an error in the result of Nashine et al. (Publ Inst Math (Beograd) (N.S.) 93(107):69–93, 2013 ). We also show that many applications of fixed point results in b -metric spaces to integral equations in the literature may be replaced by that in metric spaces.
ISSN:1578-7303
1579-1505
DOI:10.1007/s13398-016-0291-5