##
**On some generalizations of commuting mappings.**
*(English)*
Zbl 1417.54020

Summary: It is shown that occasionally \(\mathcal J \mathcal H\) operators as well as occasionally weakly biased mappings reduce to weakly compatible mappings in the presence of a unique point of coincidence (and a unique common fixed point) of the given maps.

### MSC:

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

54E40 | Special maps on metric spaces |

PDF
BibTeX
XML
Cite

\textit{M. A. Alghamdi} et al., Abstr. Appl. Anal. 2012, Article ID 952052, 6 p. (2012; Zbl 1417.54020)

Full Text:
DOI

### References:

[1] | G. Jungck, “Commuting mappings and fixed points,” The American Mathematical Monthly, vol. 83, no. 4, pp. 261-263, 1976. · Zbl 0321.54025 |

[2] | S. Sessa, “On a weak commutativity condition of mappings in fixed point considerations,” Publications Institut Mathématique, vol. 32(46), pp. 149-153, 1982. · Zbl 0523.54030 |

[3] | G. Jungck, “Compatible mappings and common fixed points,” International Journal of Mathematics and Mathematical Sciences, vol. 9, no. 4, pp. 771-779, 1986. · Zbl 0613.54029 |

[4] | G. Jungck, “Common fixed points for noncontinuous nonself maps on nonmetric spaces,” Far East Journal of Mathematical Sciences, vol. 4, no. 2, pp. 199-215, 1996. · Zbl 0928.54043 |

[5] | G. Jungck and H. K. Pathak, “Fixed points via “biased maps”,” Proceedings of the American Mathematical Society, vol. 123, no. 7, pp. 2049-2060, 1995. · Zbl 0824.47045 |

[6] | M. A. Al-Thagafi and N. Shahzad, “Generalized I-nonexpansive selfmaps and invariant approximations,” Acta Mathematica Sinica (English Series), vol. 24, no. 5, pp. 867-876, 2008. · Zbl 1175.41026 |

[7] | M. A. Al-Thagafi and N. Shahzad, “A note on occasionally weakly compatible maps,” International Journal of Mathematical Analysis, vol. 3, no. 1-4, pp. 55-58, 2009. · Zbl 1181.54045 |

[8] | M. Abbas and B. E. Rhoades, “Common fixed point theorems for occasionally weakly compatible mappings satisfying a generalized contractive condition,” Mathematical Communications, vol. 13, no. 2, pp. 295-301, 2008. · Zbl 1175.47050 |

[9] | A. Bhatt, H. Chandra, and D. R. Sahu, “Common fixed point theorems for occasionally weakly compatible mappings under relaxed conditions,” Nonlinear Analysis: Theory, Methods & Applications, vol. 73, no. 1, pp. 176-182, 2010. · Zbl 1227.47034 |

[10] | H. Bouhadjera and Ch. Godet-Thobie, “Common fixed point theorems for occasionally weakly compatible maps,” http://arxiv.org/abs/0812.3734. · Zbl 1231.54019 |

[11] | M. Imdad and A. H. Soliman, “Some common fixed point theorems for a pair of tangential mappings in symmetric spaces,” Applied Mathematics Letters, vol. 23, no. 4, pp. 351-355, 2010. · Zbl 1213.54066 |

[12] | G. Jungck and B. E. Rhoades, “Fixed point theorems for occasionally weakly compatible mappings,” Fixed Point Theory, vol. 7, no. 2, pp. 287-296, 2006. · Zbl 1118.47045 |

[13] | G. Jungck and B. E. Rhoades, “Erratum: “Fixed point theorems for occasionally weakly compatible mappings” [Fixed Point Theory, vol. 7 (2006), no. 2, 287-296],” Fixed Point Theory, vol. 9, no. 1, pp. 383-384, 2008. · Zbl 1118.47045 |

[14] | N. Hussain, M. A. Khamsi, and A. Latif, “Common fixed points for 𝒥\Bbb H-operators and occasionally weakly biased pairs under relaxed conditions,” Nonlinear Analysis: Theory, Methods & Applications, vol. 74, no. 6, pp. 2133-2140, 2011. · Zbl 1270.47042 |

[15] | L. Ciric, B. Samet, and C. Vetro, “Common fixed point theorems for families of occasionally weakly compatible mappings,” Mathematical and Computer Modelling, vol. 53, no. 5-6, pp. 631-636, 2011. · Zbl 1217.54042 |

[16] | C. Di Bari and C. Vetro, “Common fixed point theorems for weakly compatible maps satisfying a general contractive condition,” International Journal of Mathematics and Mathematical Sciences, vol. 2008, Article ID 891375, 8 pages, 2008. · Zbl 1151.54340 |

[17] | C. Vetro, “Some fixed point theorems for occasionally weakly compatible mappings in probabilistic semi-metric spaces,” International Journal of Modern Mathematics, vol. 4, no. 3, pp. 277-284, 2009. · Zbl 1221.54073 |

[18] | C. Vetro, “On Branciari’s theorem for weakly compatible mappings,” Applied Mathematics Letters, vol. 23, no. 6, pp. 700-705, 2010. · Zbl 1251.54058 |

[19] | H. K. Pathak and N. Hussain, “Common fixed points for 𝒫-operator pair with applications,” Applied Mathematics and Computation, vol. 217, no. 7, pp. 3137-3143, 2010. · Zbl 1296.47047 |

[20] | M. Abbas and G. Jungck, “Common fixed point results for noncommuting mappings without continuity in cone metric spaces,” Journal of Mathematical Analysis and Applications, vol. 341, no. 1, pp. 416-420, 2008. · Zbl 1147.54022 |

[21] | D. {\Dj}orić, Z. Kadelburg, and S. Radenović, “A note on occasionally weakly compatible mappings and common fixed points,” Fixed Point Theory. Accepted. · Zbl 1297.54110 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.