Common fixed point of a tripled power graphic \((F, \psi)\)-contraction pair on tripled partial \(b\)-metric spaces with application. (English) Zbl 07596000
Summary: The aim of this paper is to inaugurate power graphic \((F,\psi)\)-contraction pair and to establish fixed point results for such mappings defined on tripled partial \(b\)-metric spaces endowed with a graph. Then, with some examples, we will show the applications of the our results.
Keywords:
tripled partial \(b\)-metric space; directed graph; common fixed point; tripled power graphic \((F, \psi)\)-contraction pairReferences:
| [1] | Abbas, M.; Nazir, T., Common fixed point of a power graphic contraction pair in partial metric spaces endowed with a graph, Fixed Point Theory Appl., 2013, 20 (2013) · Zbl 1405.47020 · doi:10.1186/1687-1812-2013-20 |
| [2] | Abbas, M.; Nazir, T., Common fixed point of a power graphic contraction pair in partial metric spaces endowed with a graph, Fixed Point Theory Appl., 2013, 2 (2013) · Zbl 1405.47020 · doi:10.1186/1687-1812-2013-20 |
| [3] | Abbas, M.; Nazir, T.; Aydi, H., Fixed point of generalized graphic contraction mappings in partial metric spaces endowed with a graph, J. Adv. Math. Stud., 6, 2, 130-139 (2013) · Zbl 1301.54058 |
| [4] | Abbas, M.; Alfuraidan, MR; Khan, AR; Nazir, T., Fixed point results for set-contractions on metric spaces with a directed graph, Fixed Point Theory Appl., 2015, 14 (2015) · Zbl 1395.54031 · doi:10.1186/s13663-015-0263-z |
| [5] | Ali, MU; Kamran, T., Multivalued F-contraction and related fixed point theorems with applications, Filomat, 30, 14, 3779-3793 (2016) · Zbl 1461.54071 · doi:10.2298/FIL1614779A |
| [6] | Bojor, F., Fixed point of \(\varphi \)-contraction in metric spaces endowed with a graph, An. Univ. Craiova. Ser. Math. Comput. Sci., 37, 4, 85-92 (2010) · Zbl 1215.54018 |
| [7] | Gu, F.; He, Z., The common fixed point theorems for a class of twice power type \(\psi \)-contraction mapping, J. Shangqiu Teach. Coll., 22, 5, 27-33 (2006) |
| [8] | Gwóźdź-Łukawska, G.; Jachymski, J., IFS on a metric space with a graph structure and extensions of the Kelisky-Rivlin theorem, J. Math. Anal. Appl., 356, 453-463 (2009) · Zbl 1171.28002 · doi:10.1016/j.jmaa.2009.03.023 |
| [9] | Jachymski, J.; Jóźwik, I.; Jachymski, J.; Reich, S., Nonlinear contractive conditions: A comparison and related problems, Fixed Point Theory and Its Applications, 123-146 (2007), Warsaw: Banach Cent Publ, Institute of Mathematics, Warsaw · Zbl 1149.47044 · doi:10.4064/bc77-0-10 |
| [10] | Matthews, SG, Partial metric topology, Ann. N. Y. Acad. Sci., 728, 183-197 (1994) · Zbl 0911.54025 · doi:10.1111/j.1749-6632.1994.tb44144.x |
| [11] | Mukheimer, A., \( \alpha -\psi -\phi \)-contraction mappings in ordered partial \(b\)-metric spaces, J. Inequal. Appl., 7, 168-179 (2014) · Zbl 1477.54116 |
| [12] | Mustafa, Z.; Roshan, JR; Parvanesh, V.; Kadelburg, Z., Some common fixed point results in ordered partial \(b\)-metric spaces, J. Inequal. Appl., 2013, 562 (2013) · Zbl 1489.54180 · doi:10.1186/1029-242X-2013-562 |
| [13] | Piri, H.; Kumam, P., Some fixed point theorems concerning \(F\)-contraction in complete metric spaces, Fixed Point Theory Appl., 2014, 210 (2014) · Zbl 1371.54184 · doi:10.1186/1687-1812-2014-210 |
| [14] | Shukla, S., Partial \(b\)-metric spaces and fixed point theorems, Mediterr. J. Math., 11, 703-711 (2014) · Zbl 1291.54072 · doi:10.1007/s00009-013-0327-4 |
| [15] | Shukla, S.; Radenovi’c, S., Some common fixed point theorems for \(F\)-contraction type mappings in 0-complete partial metric spaces, J. Math., 2013 (2013) · Zbl 1268.54035 |
| [16] | Singh, D.; Chauhan, V.; Kumam, P.; Joshi, V., Application of cyclic Boyd-Wong type generalized \(F-\psi \)-contractions to dynamic programming, J. Math. Comput. Sci., 17, 200-215 (2017) · Zbl 1427.54069 · doi:10.22436/jmcs.017.02.02 |
| [17] | Wardowski, D., Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl., 2012, 94 (2012) · Zbl 1310.54074 · doi:10.1186/1687-1812-2012-94 |
| [18] | Wardowski, D.; Van Dung, N., Fixed points of F-weak contractions on complete metric spaces, Demonstr. Math., 42, 1, 146-155 (2014) · Zbl 1287.54046 |
| [19] | Zheng, HH; Gu, F., Some results of common fixed point for four self-maps satisfying a new \(\psi \)-contractive condition in partial metric spaces, J. Nonlinear Sci. Appl., 9, 2258-2272 (2016) · Zbl 1338.54238 · doi:10.22436/jnsa.009.05.29 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
