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Contraction principles in \(M_s\)-metric spaces. (English) Zbl 1412.47151

Summary: In this paper, we give an interesting extension of the notion of partial S-metric space which was introduced [the first author, Univers. J. Math. Math. Sci. 5, No. 2, 109–119 (2014; Zbl 1307.54049)] to the notion of \(M_s\)-metric space. Also, we prove the existence and uniqueness of a fixed point for a self-mapping on an \(M_s\)-metric space under different contraction principles.

MSC:

47H10 Fixed-point theorems
54H25 Fixed-point and coincidence theorems (topological aspects)
54E35 Metric spaces, metrizability

Citations:

Zbl 1307.54049
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References:

[1] Abdeljawad, T., Fixed points for generalized weakly contractive mappings in partial metric spaces, Math. Comput. Modelling, 54, 2923-2927 (2011) · Zbl 1237.54038 · doi:10.1016/j.mcm.2011.07.013
[2] Abdeljawad, T., Meir-Keeler \(\alpha \)-contractive fixed and common fixed point theorems, Fixed Point Theory Appl., 2013, 1-10 (2013) · Zbl 1295.54038 · doi:10.1186/1687-1812-2013-19
[3] Abdeljawad, T.; Aydi, H.; E. Karapınar, Coupled fixed points for Meir-Keeler contractions in ordered partial metric spaces, Math. Probl. Eng., 2012, 1-20 (2012) · Zbl 1264.54055 · doi:10.1155/2012/327273
[4] Abdeljawad, T.; Karapınar, E.; Taş, K., A generalized contraction principle with control functions on partial metric spaces, Comput. Math. Appl., 63, 716-719 (2012) · Zbl 1238.54017 · doi:10.1016/j.camwa.2011.11.035
[5] Altun, I.; Erduran, A., Fixed point theorems for monotone mappings on partial metric spaces, Fixed Point Theory Appl., 2011, 1-10 (2011) · Zbl 1207.54051 · doi:10.1155/2011/508730
[6] Altun, I.; Sola, F.; Simsek, H., Generalized contractions on partial metric spaces, Topology Appl., 157, 2778-2785 (2010) · Zbl 1207.54052
[7] Asadi, M.; Karapınar, E.; Salimi, P., New extension of p-metric spaces with some fixed-point results on M-metric spaces, J. Inequal. Appl., 2014, 1-9 (2014) · Zbl 1414.54015 · doi:10.1186/1029-242X-2014-18
[8] Matthews, S. G., Partial metric topology, Papers on general topology and applications, Flushing, NY, (1992), 183-197, Ann. New York Acad. Sci., 728 (1994) · Zbl 0911.54025 · doi:10.1111/j.1749-6632.1994.tb44144.x
[9] Mlaiki, N., A contraction principle in partial S-metric spaces, Univers. J. Math. Math. Appl., 5, 109-119 (2014) · Zbl 1307.54049
[10] Mlaiki, N., Common fixed points in complex S-metric space, Adv. Fixed Point Theory, 4, 509-524 (2014)
[11] N. Mlaiki, \( \alpha-\psi \)-contractive mapping on S-metric space, Math. Sci. Lett., 4, 9-12 (2015) · doi:10.12785/msl/040103
[12] Mlaiki, N.; Zarrad, A.; Souayah, N.; Mukheimer, A.; Abdeljawad, T., Fixed point theorems in \(M_b\)-metric spaces, J. Math. Anal., 7, 1-9 (2016) · Zbl 1362.54040
[13] Shoaib, A.; Arshad, M.; Ahmad, J., Fixed point results of locally contractive mappings in ordered quasi-partial metric spaces, Sci. World J., 2013, 1-8 (2013) · doi:10.1155/2013/194897
[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] Souayah, N., A fixed point in partial \(S_b\)-metric spaces, An. St. Univ. Ovidius Constanţa, 24, 351-362 (2016) · Zbl 1389.54125 · doi:10.1515/auom-2016-0062
[16] Souayah, N.; Mlaiki, N., A fixed point in \(S_b\)-metric spaces, J. Math. Comput. Sci., 16, 131-139 (2016)
[17] Valero, O., On Banach fixed point theorems for partial metric spaces, Appl. Gen. Topol., 6, 229-240 (2005) · Zbl 1087.54020 · doi:10.4995/agt.2005.1957
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