Fixed point results for Hardy--Rogers type contractions with respect to a $c$-distance in graphical cone metric spaces
Problemy analiza, Tome 9 (2020) no. 1, pp. 27-37.

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The aim of this paper is to prove some existence and uniqueness results of the fixed points for Hardy–Rogers type contraction in cone metric spaces associated with a $c$-distance and endowed with a graph. These results prepare a more general statement, since we apply the condition of orbitally $G$-continuity of mapping instead of the condition of continuity, and consider cone metric spaces endowed with a graph instead of cone metric spaces.
Keywords: cone metric spaces, fixed point, orbitally $G$-continuous, connected graph.
Mots-clés : $c$-distance
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L. Aryanpour; H. Rahimi; G. Soleimani Rad. Fixed point results for Hardy--Rogers type contractions with respect to a $c$-distance in graphical cone metric spaces. Problemy analiza, Tome 9 (2020) no. 1, pp. 27-37. http://geodesic.mathdoc.fr/item/PA_2020_9_1_a1/

[1] Alfuraidan M. R., Khamsi M. A., “Coupled fixed points of monotone mappings in a metric space with a graph”, Fixed Point Theory, 19:1 (2018), 33–44 | DOI | MR | Zbl

[2] Bondy J. A., Murty U. S. R., Graph theory, Springer, 2008 | MR | Zbl

[3] Cho Y. J., Saadati R., Wang S. H., “Common fixed point theorems on generalized distance in ordered cone metric spaces”, Comput. Math. Appl., 61 (2011), 1254–1260 | DOI | MR | Zbl

[4] Fallahi F., Petrusel A., Soleimani Rad G., “Fixed point results for pointwise Chatterjea type mappings with respect to a $c$-distance in cone metric spaces endowed with a graph”, U.P.B. Sci. Bull. (Series A), 80:1 (2018), 47–54 | MR | Zbl

[5] Fallahi K., Soleimani Rad G., “Fixed points of a $\varphi$-$G$-contractive mapping with respect to a $c$-distance on an abstract metric space endowed with a graph”, Mathematical Notes, 105:5–6 (2019), 781–788 | DOI | MR | Zbl

[6] Hardy G. H., Rogers T. D., “A generalization of a fixed point theorem of Reich”, Canad. Math. Bull., 16 (1973), 201–206 | DOI | MR | Zbl

[7] Huang H., Radenović S., Dosenović T., “Some common fixed point theorems on $c$-distance in cone metric spaces over Banach algebras”, Appl. Comput. Math., 14:2 (2015), 180–193 | MR | Zbl

[8] Huang L. G., Zhang X., “Cone metric spaces and fixed point theorems of contractive mappings”, J. Math. Anal. Appl., 332 (2007), 1467–1475 | DOI | MR

[9] Jachymski J., “The contraction principle for mappings on a metric space with a graph”, Proc. Amer. Math. Soc., 136 (2008), 1359–1373 | DOI | MR | Zbl

[10] Jleli M., C̆ojbas̆ić Rajić V., Samet B., Vetro C., “Fixed point theorems on ordered metric spaces and applications to nonlinear elastic beam equations”, J. Fixed Point Theory Appl., 12 (2012), 175–192 | DOI | MR | Zbl

[11] Kada O., Suzuki T., Takahashi W., “Nonconvex minimization theorems and fixed point theorems in complete metric spaces”, Math. Japon., 44 (1996), 381–391 | MR | Zbl

[12] Nicolae A., O'Regan D., Petrusel A., “Fixed point theorems for singlevalued and multivalued generalized contractions in metric spaces endowed with a graph”, Georgian Math. J., 18 (2011), 307–327 | MR | Zbl

[13] Petrusel A., Rus I. A., “Fixed point theorems in ordered $L$-spaces”, Proc. Amer. Math. Soc., 134:2 (2006), 411–418 | DOI | MR | Zbl

[14] Petrusel A., Rus I. A., “Fixed point theory in terms of a metric and of an order relation”, Fixed Point Theory, 20:2 (2019), 601–622 | DOI | MR

[15] Rahimi H., Soleimani Rad G., “Common fixed-point theorems and $c$-distance in ordered cone metric spaces”, Ukrain. Math. J., 65:12 (2014), 1845–1861 | DOI | MR | Zbl

[16] Soleimani Rad G., Rahimi H., Vetro C., “Fixed point results under generalized $c$-distance with application to nonlinear fourth-order differential equation”, Fixed Point Theory, 20:2 (2019), 635–648 | DOI | MR

[17] Wang S., Guo B., “Distance in cone metric spaces and common fixed point theorems”, Appl. Math. Lett., 24 (2011), 1735–1739 | DOI | MR | Zbl

[18] Zabrejko P. P., “$K$-metric and $K$-normed linear spaces: survey”, Collect. Math., 48 (1997), 825–859 | MR | Zbl