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Reciprocal continuity and common fixed points of nonself mappings. (English) Zbl 1189.47054

The notions of reciprocal continuity and \(C_q\)-commutativity are extended to the nonself setting, apart from observing the equivalence between compatibility and \(\varphi\)-compatibility. The authors then obtain some results on coincidence and common fixed points for two pairs of nonself mappings in metrically convex metric spaces. A common fixed point theorem in Banach spaces is also proved as an application of the main result. Some interesting illustrative examples are provided.
Reviewer’s remarks:
Page 1457, Line 1 from bottom, should read “prove some fixed point theorems in metric spaces…”.
Page 1459, Line 7 from top, should read “is a function which satisfies (i), (ii) and (iii).”
Page 1459, Line 7 from bottom, should read ”to prove some common fixed point theorems…”.
Page 1466, Line 11 from top, should read “The uniqueness of \(G_z\) easily follows from (1.1.1).”

MSC:

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