Sentence examples for notion of compatibility from inspiring English sources

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 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.

Choudhury and Kundu [7] give a notion of compatibility.

Note that Definition 1.12 extends and generalizes the notion of compatibility introduced by Jungck [25].

Weak commutativity is essentially a point property, while the notion of compatibility uses the machinery of sequences.

Recently, the notion of compatibility of F and g was defined by Choudhury and Kundu [12] as follows.

We consider two classic versions of the supertree problem, based on the closely related notions of compatibility and agreement.

Hence, the notion of weak compatibility is more general than compatibility.

The mechanisms obtained via this framework are randomized, and obtain incentive compatibility in the universal sense (in contrast to the substantially weaker notion of incentive compatibility in expectation).

In [40] Pant and Bisht introduced the notion of conditional compatibility which does not require such a precondition and yet is a proper generalization of both nontrivial compatibility and subcompatibility.

Finally, using the notion of weak compatibility of the pair together with (1.6), we get.