The phrase "a pair of weakly" is not correct in standard written English as it lacks a noun to complete the expression.
It could be used in a context where you are describing two items or entities that are weak in some manner, but it needs to be followed by a noun.
Example: "The researchers observed a pair of weakly interacting particles during the experiment."
Alternatives: "a couple of feeble" or "two weak".
While, Nashine and Samet [12] proved some new coincidence point theorems for a pair of weakly increasing mappings.
In this section, we prove common endpoint theorems for a pair of weakly isotone increasing multivalued mappings under a generalized -weak contractive condition.
( S, T ) is a pair of weakly increasing mappings with respect to R ; 4. ( S, T ) is a pair of dominating maps; 5.
Nashine et al. [26] proved some new coincidence point and common fixed point theorems for a pair of weakly increasing mappings with respect to another map.
Very recently, Shatanawi and Samet [33] proved some coincidence point theorems for a pair of weakly increasing mappings with respect to another map.
Four common fixed point theorems for a pair of weakly compatible mappings satisfying contractive conditions of integral type in metric spaces are proved.
Next, the singularity-reduced integral equations obtained for an isolated crack are extended to allow treatment of cracks in a finite domain, and a pair of weakly-singular, weak-form displacement and traction integral equations is established.
The roughly triangular shape of the distribution is expected for a pair of weakly-interacting freely-jointed segments.
If it is a pair of occasionally weakly g-biased mappings, then it is WC.
As ( I, T ) is a pair of partially weakly increasing mappings, I f 2 n ≤ T ( I f 2 n ) and f 2 n − 1 ≤ T f 2 n − 1 = I f 2 n ≤ T ( I f 2 n ).
Hence, u is a common fixed point of f, g, S, and T. In the following result, we establish existence of a common fixed point for a pair of partially weakly increasing functions on an ordered metric space by using a control function r : R+ → R+.
