Geodesic
Fixed point belonging to the zero-set of a given function
Vetro, Francesca 1
1 Nonlinear Analysis Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam;Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam
Journal of nonlinear sciences and its applications, Tome 11 (2018) no. 3, p. 417-424.

Voir la notice de l'article provenant de la source International Scientific Research Publications

We prove the existence and uniqueness of fixed point belonging to the zero-set of a given function. The results are established in the setting of metric spaces and partial metric spaces. Our approach combines the recent notions of $(F,\varphi)$-contraction and $\mathcal{Z}$-contraction. The main result allows to deduce, as a particular case, some of the most known results in the literature. An example supports the theory.
DOI : 10.22436/jnsa.011.03.09
Classification : 47H10, 54H25
Keywords: Fixed point, metric space, partial metric space, nonlinear contraction, simulation function

Vetro, Francesca  1

1 Nonlinear Analysis Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam;Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam 
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Vetro, Francesca . Fixed point belonging to the zero-set of a given function. Journal of nonlinear sciences and its applications, Tome 11 (2018) no. 3, p. 417-424. doi : 10.22436/jnsa.011.03.09. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.011.03.09/

[1] Banach, S. Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math., Volume 3 (1922), pp. 133-181

[2] Boyd, D. W.; Wong, J. S. W. On nonlinear contractions, Proc. Amer. Math. Soc., Volume 20 (1969), pp. 458-464

[3] Jleli, M.; Samet, B.; Vetro, C. Fixed point theory in partial metric spaces via \(\varphi\)-fixed point’s concept in metric spaces, J. Inequal. Appl., Volume 2014 (2014), pp. 1-9 | Zbl | DOI

[4] Khojasteh, F.; Shukla, S.; Radenović, S. A new approach to the study of fixed point theorems via simulation functions, Filomat, Volume 29 (2015), pp. 1189-1194

[5] Matthews, S. G. Partial metric topology, in: Proc. 8th Summer Conference on General Topology and Applications, Ann. New York Acad. Sci., Volume 728 (1994), pp. 183-197 | DOI

[6] O’Neill, S. J. Partial metrics, valuations and domain theory, in: Proc. 11th Summer Conference on General Topology and Applications, Ann. New York Acad. Sci. , Volume 806 (1996), pp. 304-315 | DOI

[7] Paesano, D.; Vetro, P. Suzuki’s type characterizations of completeness for partial metric spaces and fixed points for partially ordered metric spaces, Topology Appl., Volume 159 (2012), pp. 911-920 | DOI | Zbl

[8] Reich, S. Fixed points of contractive functions, Boll. Un. Mat. Ital., Volume 5 (1972), pp. 26-42

[9] Rhoades, B. E. Some theorems on weakly contractive maps, Nonlinear Anal., Volume 47 (2001), pp. 2683-2693 | DOI

[10] Samet, B.; Vetro, C.; Vetro, F. From metric spaces to partial metric spaces, Fixed Point Theory Appl., Volume 2013 (2013 ), pp. 1-11 | DOI

[11] Vetro, C.; Vetro, F. Metric or partial metric spaces endowed with a finite number of graphs: a tool to obtain fixed point results, Topology Appl., Volume 164 (2014), pp. 125-137 | Zbl | DOI

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