Reciprocal continuity and common fixed points of nonself mappings (Q1039527)

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\dots''. 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\dots''. Page 1466, Line 11 from top, should read ``The uniqueness of \(G_z\) easily follows from (1.1.1).''