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Common fixed point theorems for \(R\)-weakly commuting mappings of type \((A_f)\). (English) Zbl 1071.54502

Summary: We obtain some fixed point theorems for non-compatible mappings. We study some consequences of the recently introduced notion of \(R\)-weak commutativity of type \((A_f)\) by H. K. Pathak, Y. J. Cho and S. M. Kang, Bull. Korean Math. Soc. 34, 247–257 (1997; Zbl 0878.54032)]. These theorems employ the notion of pointwise \(R\)-weak commutativity of type \((A_f)\), which is a necessary condition for the existence of a common fixed point of contractive type mappings.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)

Citations:

Zbl 0878.54032
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