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Hybrid tangential property and coincidence point theorems. (English) Zbl 1179.47045

Let \((X,d)\) be a metric space, and \(f,g:X\to X\), \(F,G:X\to CL(X)\) be two pairs of maps. The hybrid pair \((f,T)\) is called \(g\)-tangential at \(t\in X\) if there exist two sequences \((x_n)\) \((y_n)\) in \(X\) and \(A\in CL(X)\) with \(t\in A\), such that \(\lim_n(fx_n)=\lim_n(gy_n)=t\), \(\lim_n(Tx_n)=A\) and \(\lim_n(Sy_n)\in CL(X)\). This is a weaker version of the common property (E,A) in [Y.-C.Liu, J.Wu and Z.-X.Li, Int.J.Math.Math.Sci.2005, No.19, 3045–3055 (2005; Zbl 1087.54019)]. The authors show that such a property will suffice in proving the main results of the quoted paper (based on the common property (E,A)).

MSC:

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

Citations:

Zbl 1087.54019
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