×

Quasi-partial \(b\)-metric spaces and some related fixed point theorems. (English) Zbl 1347.54081

Summary: In this paper, the quasi-partial \(b\)-metric space is defined and general fixed point theorems on this space are discussed with examples.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54E40 Special maps on metric spaces

References:

[1] Czerwik, S: Contraction mappings in b-metric spaces. Acta Math. Inform. Univ. Ostrav. 1, 5-11 (1993) · Zbl 0849.54036
[2] Mukheimer, A: α-ψ-ϕ-Contractive mappings in ordered partial b-metric spaces. J. Nonlinear Sci. Appl. 7, 168-179 (2014) · Zbl 1477.54116
[3] Shatanawi, W: On ω-compatible mappings and common coupled coincidence point in cone metric spaces. Appl. Math. Lett. 25, 925-931 (2012) · Zbl 1241.54038 · doi:10.1016/j.aml.2011.10.037
[4] Bhaskar, TG, Lakshmikantham, V: Fixed point theorems in partially ordered metric spaces and applications. Nonlinear Anal. 65, 1379-1393 (2006) · Zbl 1106.47047 · doi:10.1016/j.na.2005.10.017
[5] Lakshmikantham, V, Ćirić, L: Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces. Nonlinear Anal. 70, 4341-4349 (2009) · Zbl 1176.54032 · doi:10.1016/j.na.2008.09.020
[6] Hicks, TL: Fixed point theorems for quasi-metric spaces. Math. Jpn. 33(2), 231-236 (1988) · Zbl 0642.54047
[7] Karapınar, E: Generalizations of Caristi Kirk’s theorem on partial metric spaces. Fixed Point Theory Appl. 2011, Article ID 4 (2011) · Zbl 1281.54027 · doi:10.1186/1687-1812-2011-4
[8] Ali, MU: Mizoguchi-Takahashi’s type common fixed point theorem. J. Egypt. Math. Soc. 22, 272-274 (2014) · Zbl 1298.54026 · doi:10.1016/j.joems.2013.08.004
[9] Bakhtin, IA, The contraction principle in quasimetric spaces, No. 30, 26-37 (1989) · Zbl 0748.47048
[10] Bota, M-F, Karapınar, E, Mleşniţe, O: Ulam-Hyers stability results for fixed point problems via α-ψ-contractive mapping in (b)-metric space. Abstr. Appl. Anal. 2013, Article ID 825293 (2013) · Zbl 1434.54013 · doi:10.1155/2013/825293
[11] Bota, M-F, Karapınar, E: A note on ‘Some results on multi-valued weakly Jungck mappings in b-metric space’. Cent. Eur. J. Math. 11(9), 1711-1712 (2013) · Zbl 1294.47075 · doi:10.2478/s11533-013-0272-2
[12] Aydi, H, Bota, M-F, Karapınar, E, Moradi, S: A common fixed point for weak ϕ-contractions ON b-metric spaces. Fixed Point Theory 13(2), 337-346 (2012) · Zbl 1297.54080
[13] Aydi, H, Bota, M-F, Karapınar, E, Mitrović, S: A fixed point theorem for set-valued quasi-contractions in b-metric spaces. Fixed Point Theory Appl. 2012, Article ID 88 (2012) · Zbl 1457.54032 · doi:10.1186/1687-1812-2012-88
[14] Latif, A, Al-Mezel, SA: Fixed point results in quasi metrics spaces. Fixed Point Theory Appl. 2011, Article ID 178306 (2011) · Zbl 1207.54061 · doi:10.1155/2011/178306
[15] 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
[16] Caristi, J: Fixed point theorems for mapping satisfying inwardness conditions. Trans. Am. Math. Soc. 215, 241-251 (1976) · Zbl 0305.47029 · doi:10.1090/S0002-9947-1976-0394329-4
[17] Karapınar, E, Erhan, ÍM, Özturk, A: Fixed point theorems on quasi-partial metric spaces. Math. Comput. Model. 57, 2442-2448 (2013) · Zbl 1286.54045 · doi:10.1016/j.mcm.2012.06.036
[18] Shatanawi, W, Pitea, A: Some coupled fixed point theorems in quasi-partial metric spaces. Fixed Point Theory Appl. 2013, Article ID 153 (2013). doi:10.1186/1637-1812-2013-153 · Zbl 1318.54036 · doi:10.1186/1637-1812-2013-153
[19] Matthews, SG: Partial metric topology, general topology and its applications. Ann. N.Y. Acad. Sci. 728, 183-197 (1994) · Zbl 0911.54025 · doi:10.1111/j.1749-6632.1994.tb44144.x
[20] Altun, I, Erduran, A: Fixed point theorems, for monotone mappings on partial metric spaces. Fixed Point Theory Appl. 2011, Article ID 508730 (2011) · Zbl 1207.54051 · doi:10.1155/2011/508730
[21] Matthews, SG: Partial Metric Topology. Research Report 212, Department of Computer Science, University of Warwick (1992) · Zbl 0305.47029
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.