Some writers defend a less austere version of this model, by weakening the notion of validity.
In 2008, Al-Thagafi and Shahzad [6] weakened the notion of nontrivial weakly compatible maps by introducing a new notion of occasionally weakly compatible (in short, owc) maps.
Further, Singh and Jain [5] weakened the notion of compatibility by using the notion of weakly compatible mappings in fuzzy metric spaces and showed that every pair of compatible mappings is weakly compatible but reverse is not true.
Jungck further weakens the notion of compatibility by introducing the notion of weak compatibility and in [16] Jungck and Rhoades further extended weak compatibility to the setting of single-valued and multivalued maps.
Jungck and Rhoades [22] weakened the notion of compatibility by introducing the notion of weakly compatible mappings (extended by Singh and Jain [23] to probabilistic metric space) and proved common fixed-point theorems without assuming continuity of the involved mappings in metric spaces.
Then f x n → 2, g x n → 2, f g x n → 2 = g 2, g f x n → 4, lim n d ( f g x n, g t ) = 0, f g 2 = g f 2 and lim n d ( f g x n, g f x n ) ≠ 0. In 1997, Pathak et al. [49] weakened the notion of compatible of type ( A ) by splitting it into two parts, namely f-compatible and g-compatible.
This further highlights the complexity of Hsp90 inhibitor effects and weakens the notion that variations of HIF-α isoform stability is a primary reason for the clinical failure of these agents [ 34].
Alam et al. [10] further weakened the notions embodied in Definition 1 as follows.
Relational interpretations of quantum mechanics propose a solution to the interpretational difficulties of quantum theory based on the idea of weakening the notions of the state of a system, event, and the idea that a system, at a certain time, may just have a certain property.
By creating tensions between anti-WMD and sovereignty norms, chemical weapons are especially pernicious at opening the door to R2P arguments that weaken the fundamental notion of sovereignty.
