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Some common fixed-point theorems for generalized-contractive-type mappings on complex-valued metric spaces. (English) Zbl 1272.54038

Summary: Fixed-point theory in complex valued metric spaces has greatly developed in recent times. In this paper, we prove certain common fixed-point theorems for two single-valued mappings in such spaces. The mappings we consider here are assumed to satisfy certain metric inequalities with generalized fixed-point theorems due to F. Rouzkard and M. Imdad [Comput. Math. Appl. 64, No. 6, 1866–1874 (2012; Zbl 1268.54033)]. This extends and subsumes many results of other authors which were obtained for mappings on complex-valued metric spaces.

MSC:

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

Citations:

Zbl 1268.54033
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References:

[1] Banach, S., Sur les operations dans les ensembles abstraits et leur application aux equations integrales, Fundamenta Mathematicae, 3, 133-181 (1992)
[2] 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 · doi:10.1080/01630563.2011.533046
[3] Mohanta, S. K.; Maitra, R., Common fixed point of three self mappings in complex valued metric spaces, International Journal of Mathematical Archive, 3, 8, 2946-2953 (2012)
[4] Sintunavarat, W.; Kumam, P., Generalized common fixed point theorems in complex valued metric spaces and applications, Journal of Inequalities and Applications, 2012, article 84 (2012) · Zbl 1295.54090 · doi:10.1186/1029-242X-2012-84
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[6] Rouzkard, F.; Imdad, M., Some common fixed point theorems on complex valued metric spaces, Computers & Mathematics with Applications, 64, 6, 1866-1874 (2012) · Zbl 1268.54033 · doi:10.1016/j.camwa.2012.02.063
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