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Well-posedness and periodic point property of mappings satisfying a rational inequality in an ordered complex valued metric space. (English) Zbl 1289.54108

Summary: A. Azam, B. Fisher and M. Khan [Numer. Funct. Anal. Optim. 32, No. 3, 243–253 (2011; Zbl 1245.54036), corrigendum ibid. 33, No. 5, 590 (2012; Zbl 1242.54019)] introduced a notion of complex valued metric space and obtained common fixed point result for mappings in the context of complex valued metric spaces. In this paper, employing the concept of weakly increasing mappings, the existence of common fixed points is obtained in an ordered complex valued metric space. We apply our results to study well-posedness of a common fixed point problem for two rational type contractive mappings and a periodic point property of mapping involved therein.

MSC:

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