Geodesic
On some generalized contractive maps in partial metric space and related fixed point theorems
Filomat, Tome 36 (2022) no. 19, p. 6539

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DOI

In this paper we generalize some results of fixed point theory to partial metric spaces by using metric methods in the context of a new extension of Ekeland's variational principle. We provide some corollaries to unify our results with other existing results in the literature along the same vein. Then, we show that our results require existence assumptions weaker than those for some well-known contractive maps, including the ones in the sense of Banach, Ćirić, Song, Kannan and Hardy Rogers. Also, we provide some estimates for the distance to the fixed point set in partial metric space. In order to illustrate the strength of our fixed point theorem, we use it in order to derive a new result on coupled fixed points.
DOI : 10.2298/FIL2219539B
Classification : 46T99, 47H10, 54H25
Keywords: partial metric space, generalized contractive maps, Ekeland’s variational principle, fixed point 
Abdelkader Belhenniche; Sfya Benahmed; Liliana Guran; Fernando Lobo Pereira. On some generalized contractive maps in partial metric space and related fixed point theorems. Filomat, Tome 36 (2022) no. 19, p. 6539 . doi: 10.2298/FIL2219539B
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     title = {On some generalized contractive maps in partial metric space and related fixed point theorems},
     journal = {Filomat},
     pages = {6539 },
     year = {2022},
     volume = {36},
     number = {19},
     doi = {10.2298/FIL2219539B},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2219539B/}
}
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