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Employing common limit range property to prove unified metrical common fixed point theorems. (English) Zbl 1268.54024
Summary: The purpose of this paper is to emphasize the role of “common limit range property” to ascertain the existence of common fixed point in metric spaces satisfying an implicit function essentially due to J. Ali and M. Imdad [Sarajevo J. Math. 4(17), No. 2, 269–285 (2008; Zbl 1180.54052)]. As an application to our main result, we derive a fixed point theorem for four finite families of self-mappings which can be utilized to derive common fixed point theorems involving any finite number of mappings. Our results improve and extend a host of previously known results including the ones contained in the paper of Ali and Imdad [loc. cit.]. We also furnish some illustrative examples to support our main results.

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