From: A comparison of various noncommuting conditions in metric fixed point theory and their applications
S. No. | Forms | Year | References |
---|---|---|---|
1. | weakly commuting mappings | 1982 | Sessa [42] |
2. | asymptotically commuting mappings | 1986 | Tivari and Singh [31] |
3. | compatible mappings | 1986 | Jungck [30] |
4. | weakly∗ commuting mappings | 1986 | Pathak [32] |
5. | weakly uniformly contraction mappings | 1990 | Pathak [43] |
6. | weakly∗∗ commuting mappings | 1992 | Pathak [33] |
7. | compatible mappings of type (A) | 1993 | Jungck et al. [34] |
8. | preorbitally commuting mappings | 1994 | Singh and Mishra [44] |
9. | R-weakly commuting mappings | 1994 | Pant [36] |
10. | pointwise R-weakly commuting mappings | 1994 | Pant [36] |
11. | biased and weakly g-biased mappings | 1995 | Jungck and Pathak [35] |
12. | semi-compatible mappings | 1995 | Cho et al. [45] |
13. | compatible mappings of type (B) | 1995 | Pathak and Khan [46] |
14. | compatible mappings of type (P) | 1995 | Pathak et al. [47] |
15. | compatible mappings of type (f) or type (g) | 1995 | Pathak et al. [48] |
16. | weakly compatible mappings | 1996 | Jungck [29] |
17. | f-compatible or g-compatible mappings | 1997 | Pathak and Khan [49] |
18. | R-weakly commuting mappings of type or | 1997 | Pathak et al. [50] |
19. | g-biased mappings of type (A) | 1998 | Pathak et al. [51] |
20. | compatible mappings of type (C) | 1998 | Pathak et al. [52] |
21. | biased mappings of type or | 1999 | Fisher and Murthy [53] |
22. | coincidentally commuting mappings | 1999 | Dhage [54] |
23. | partially commuting mappings | 2000 | Sastry et al. [55] |
24. | compatible mappings of type (N) | 2000 | Srivastava et al. [56] |
25. | intimate mappings | 2001 | Sahu et al. [57] |
26. | compatible mappings of type (C) | 2002 | Singh [58] |
27. | weakly compatible mappings of type (f) or type (g) | 2007 | Pathak and Ume [59] |
28. | occasionally weakly compatible mappings | 2008 | Al-Thagafi and Shahzad [38] |
29. | Banach operator pairs | 2007 | Chen and Li [60] |
30. | conditionally commuting mappings | 2009 | Pant and Pant [61] |
31. | subcompatible mappings | 2009 | Bouhadjera and Godet-Thobie [62] |
32. | P-operators | 2010 | Pathak and Hussain [63] |
33. | almost compatible and almost biased mappings | 2010 | Suzuki and Pathak [64] |
34. | Ï•-weakly compatible of type (f, g) | 2011 | Pathak and Tiwari [65] |
35. | JH-operators | 2011 | Hussain et al. [39] |
36. | conditionally compatible mappings | 2012 | Pant and Bisht [40] |
37. | occasionally weakly biased pairs | 2011/2012 | |
38. | pseudo compatible mappings | 2013 | Pant and Bisht [67] |
39. | PD-operators | 2013 | Pathak and Rai [37] |
40. | faintly compatible | 2013 | Bisht and Shahzad [41] |