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Agarwal, Ravi P.; Alsulami, Hamed H.; Karapınar, Erdal; Khojasteh, Farshid

Remarks on some recent fixed point results on quaternion-valued metric spaces. (English) Zbl 1469.54034

Abstr. Appl. Anal. 2014, Article ID 171624, 8 p. (2014).
Summary: In [ibid. 2014, Article ID 258985, 9 p. (2014; Zbl 1469.54091)], A. El-Sayed Ahmed et al. introduced the notion of quaternion-valued metric as a generalization of metric and proved a common fixed point theorem in the context of quaternion-valued metric space. In this paper, we will show that the quaternion-valued metric spaces are subspaces of cone metric spaces. Consequently, the fixed point results in such spaces can be derived as a consequence of the corresponding existing fixed point result in the setting cone metric spaces.

Cited in 4 Documents

MSC:

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

Citations:

Zbl 1469.54091
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\textit{R. P. Agarwal} et al., Abstr. Appl. Anal. 2014, Article ID 171624, 8 p. (2014; Zbl 1469.54034)
Full Text: DOI

References:

[1] Azam, A.; Fisher, B.; Khan, M., Common fixed point theorems in complex valued metric spaces, Numerical Functional Analysis and Optimization, 32, 3, 243-253 (2011) · Zbl 1245.54036
[2] Ahmed, A. E.-S.; Asad, A. J.; Omran, S., Fixed point theorems in quaternion-valued metric spaces, Abstract and Applied Analysis, 2014 (2014) · Zbl 1469.54091
[3] Du, W.-S., A note on cone metric fixed point theory and its equivalence, Nonlinear Analysis: Theory, Methods & Applications, 72, 5, 2259-2261 (2010) · Zbl 1205.54040
[4] Abdeljawad, T.; Karapinar, E., A gap in the paper “a note on cone metric fixed point theory and its equivalence” [Nonlinear Anal. 72(5), (2010), 2259-2261], Gazi University Journal of Science, 24, 2, 233-234 (2011)
[5] Khamsi, M. A., Remarks on cone metric spaces and fixed point theorems of contractive mappings, Fixed Point Theory and Applications, 2010 (2010) · Zbl 1194.54065
[6] Amini-Harandi, A.; Fakhar, M., Fixed point theory in cone metric spaces obtained via the scalarization method, Computers & Mathematics with Applications, 59, 11, 3529-3534 (2010) · Zbl 1197.54055
[7] Feng, Y.; Mao, W., The equivalence of cone metric spaces and metric spaces, Fixed Point Theory, 11, 2, 259-263 (2010) · Zbl 1221.54055
[8] Janković, S.; Kadelburg, Z.; Radenović, S., On cone metric spaces: a survey, Nonlinear Analysis: Theory, Methods & Applications, 74, 7, 2591-2601 (2011) · Zbl 1221.54059
[9] Kadelburg, Z.; Radenović, S.; Rakočević, V., A note on the equivalence of some metric and cone metric fixed point results, Applied Mathematics Letters, 24, 3, 370-374 (2011) · Zbl 1213.54067
[10] Huang, L.-G.; Zhang, X., Cone metric spaces and fixed point theorems of contractive mappings, Journal of Mathematical Analysis and Applications, 332, 2, 1468-1476 (2007) · Zbl 1118.54022
[11] Rezapour, S.; Haghi, R. H., Some notes on the paper ‘cone metric spaces and fixed point theorems of contractive mappings’, Journal of Mathematical Analysis and Applications, 345, 2, 719-724 (2008) · Zbl 1145.54045
[12] Hadžić, O.; Gajić, L., Coincidence points for set-valued mappings in convex metric spaces, Univerzitet u Novom Sadu. Zbornik Radova Prirodno-Matematičkog Fakulteta, 16, 1, 13-25 (1986) · Zbl 0639.54037
[13] Karapınar, E., Couple fixed point theorems for nonlinear contractions in cone metric spaces, Computers & Mathematics with Applications, 59, 12, 3656-3668 (2010) · Zbl 1198.65097
[14] Abdeljawad, T.; Karapinar, E., Quasicone metric spaces and generalizations of Caristi Kirk’s theorem, Fixed Point Theory and Applications, 2009 (2009) · Zbl 1197.54051
[15] Karapınar, E., Some nonunique fixed point theorems of Ćirić type on cone metric spaces, Abstract and Applied Analysis, 2010 (2010) · Zbl 1194.54064
[16] Khojsteh, F.; Razani, A.; Moradi, S., A fixed point of generalized \(T_F\)-contraction mappings in cone metric spaces, Fixed Point Theory and Applications, 2011, article 14 (2011) · Zbl 1281.54029
[17] Assad, N. A.; Kirk, W. A., Fixed point theorems for set-valued mappings of contractive type, Pacific Journal of Mathematics, 43, 553-562 (1972) · Zbl 0239.54032
[18] Chen, G.-Y.; Huang, X. X.; Yang, X. Q., Vector Optimization (2005), Berlin, Germany: Springer, Berlin, Germany · Zbl 1105.90079
[19] Du, W.-S., On some nonlinear problems induced by an abstract maximal element principle, Journal of Mathematical Analysis and Applications, 347, 2, 391-399 (2008) · Zbl 1148.49013
[20] Du, W.-S., The existence of cone critical point and common fixed point with applications, Journal of Applied Mathematics, 2011 (2011) · Zbl 1304.54077
[21] 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 and Applications, 2012, article 88 (2012) · Zbl 1457.54032
[22] Aydi, H.; Bota, M.-F.; Karapinar, E.; Moradi, S., A common fixed point for weak \(\varphi \)-contractions on \(b\)-metric spaces, Fixed Point Theory, 13, 2, 337-346 (2012) · Zbl 1297.54080
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