Sentence examples for weak compatibility from inspiring English sources

Since f z = g z and f and g are weakly compatible, we obtain, by the definition of weak compatibility, that f g z = g f z.

To study common fixed points, Jungck [19] initiated the concept of weak compatibility of maps thus: (f_{1}) and (f_{2}) on Y are weakly compatible maps if (f_{1}f_{2}w=f_{2}f_{1}wheneverver (f_{1}w=f_{2}w), for some (win Y).

In 1996, Jungck [4] introduced the concept of weak compatibility.

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

Now, using the notion of the weak compatibility of the pair and (3.5), we get.

In 1998, Jungck and Rhoades [16] introduced the following concept of weak compatibility.

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

Note that commutativity implies weak commutativity, weak commutativity implies compatibility, and compatibility implies weak compatibility.

The weak compatibility or R-weak commutativity of the pair (T, f) implies that (2.1) holds.

Next, we need to show the weak compatibility of the pair ((f_{1},f_{3})).

By weak compatibility, we get (mathscr{V}omega =mathscr{U}omega ).