Geodesic
Dass and Gupta's fixed point theorem in $\mathcal{F}$-metric spaces
Lateef, Durdana 1 ; Ahmad, Jamshaid 2
1 Department of Mathematics, College of Science, Taibah University, Al Madina Al Munawara, 41411, Kingdom of Saudi Arabia
2 Department of Mathematics, University of Jeddah, P. O. Box 80327, Jeddah 21589, Saudi Arabia
Journal of nonlinear sciences and its applications, Tome 12 (2019) no. 6, p. 405-411.

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

The purpose of this article is to define Dass and Gupta's contraction in the context of $\mathcal{F}$-metric spaces and obtain some new fixed point theorems to elaborate, generalize and synthesize several known results in the literature including Jleli and Samet [M. Jleli, B. Samet, J. Fixed Point Theory Appl., $\textbf{20}$ (2018), 20 pages] and Dass and Gupta [B. K. Dass, S. Gupta, Indian J. Pure Appl. Math., $\textbf{6}$ (1975), 1455--1458]. Also we have provided a non trivial example to validate our main result.
DOI : 10.22436/jnsa.012.06.06
Classification : 47H10, 54H25
Keywords: \(\mathcal{F}\)-metric space, fixed point, rational contraction

Lateef, Durdana  1 ; Ahmad, Jamshaid  2

1 Department of Mathematics, College of Science, Taibah University, Al Madina Al Munawara, 41411, Kingdom of Saudi Arabia
2 Department of Mathematics, University of Jeddah, P. O. Box 80327, Jeddah 21589, Saudi Arabia 
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Lateef, Durdana ; Ahmad, Jamshaid . Dass and Gupta's fixed point theorem in \(\mathcal{F}\)-metric spaces. Journal of nonlinear sciences and its applications, Tome 12 (2019) no. 6, p. 405-411. doi : 10.22436/jnsa.012.06.06. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.012.06.06/

[1] Alnaser, L. A.; Lateef, D.; Fouad, H. A.; Ahmad, J. Relation theoretic contraction results in F-metric spaces, J. Nonlinear Sci. Appl., Volume 12 (2019), pp. 337-344

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

[3] Dass, B. K.; Gupta, S. An extension of Banach contraction principle through rational expression, Indian J. Pure Appl. Math., Volume 6 (1975), pp. 1455-1458

[4] Hussain, A.; Kanwal, T. Existence and uniqueness for a neutral differential problem with unbounded delay via fixed point results, Tran. A. Razmadze Math. Inst., Volume 172 (2018), pp. 481-490 | DOI

[5] D. S. Jaggi Some unique fixed point theorems, Indian J. Pure Appl. Math., Volume 8 (1977), pp. 223-230

[6] Jleli, M.; Samet, B. On a new generalization of Metric Spaces, J. Fixed Point Theory Appl., Volume 20 (2018), pp. 1-20 | DOI

[7] Khan, M. S. A fixed point theorem for metric spaces, Rend. Ist. Mat. Univ. Trieste, Volume 8 (1976), pp. 69-72

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