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Chauhan, Sunny; Khan, M. Alamgir; Sintunavarat, Wutiphol

Common fixed point theorems in fuzzy metric spaces satisfying \(\phi\)-contractive condition with common limit range property. (English) Zbl 1470.54047

Abstr. Appl. Anal. 2013, Article ID 735217, 14 p. (2013).
Summary: The objective of this paper is to emphasize the role of “common limit range property” to ascertain the existence of common fixed point in fuzzy metric spaces. Some illustrative examples are furnished which demonstrate the validity of the hypotheses and degree of utility of our results. 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. As an application to our main result, we prove an integral-type fixed point theorem in fuzzy metric space. Our results improve and extend a host of previously known results including the ones contained in [M. Imdad et al., J. Nonlinear Anal. Optim. 3, No. 2, 225–237 (2012; Zbl 1394.54023)].

Cited in 9 Documents

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54A40 Fuzzy topology
47H10 Fixed-point theorems

Citations:

Zbl 1394.54023
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Full Text: DOI
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References:

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