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On coincidence and fixed-point theorems in symmetric spaces. (English) Zbl 1169.54020

Summary: We give an axiom (C.C) in symmetric spaces and investigate the relationships between (C.C) and axioms (W3), (W4), and (H.E). We give some results on coinsidence and fixed-point theorems in symmetric spaces, and also some counterexamples for the results of M. Imdad, J. Ali and L. Khan [J. Math. Anal. Appl. 320, No. 1, 352–360 (2006), corrigendum ibid. 329, No. 1, 752 (2007; Zbl 1098.54033)].

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54E25 Semimetric spaces

Citations:

Zbl 1098.54033
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References:

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[5] Imdad M, Ali J, Khan L: Coincidence and fixed points in symmetric spaces under strict contractions. Journal of Mathematical Analysis and Applications 2006, 320(1):352-360. 10.1016/j.jmaa.2005.07.004 · Zbl 1098.54033 · doi:10.1016/j.jmaa.2005.07.004
[6] Aliouche A: A common fixed point theorem for weakly compatible mappings in symmetric spaces satisfying a contractive condition of integral type. Journal of Mathematical Analysis and Applications 2006, 322(2):796-802. 10.1016/j.jmaa.2005.09.068 · Zbl 1111.47046 · doi:10.1016/j.jmaa.2005.09.068
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