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We can see that there are numerous possible operating points for TX I and TX II in W. The Nash bargaining solution (NBS), defined as follows, provides a unique, fair and efficient operating point in W with the idea that after the minimal requirements are satisfied for both transmitters, the rest of the resources are allocated proportionally to each of them according to their conditions.
If we choose and (with ), since and it is not difficult to prove that (H8) is satisfied for and (H9) is satisfied if.
Remark 1 It is clear that the inequality (2.4) is satisfied for any function y satisfying the imposed assumptions.
end{aligned} (18) As (18) is satisfied for every (uin T_{n}x) and (v in T_{n} y), inequality (17) is satisfied too.
Then (2.20) has one positive solution in if either of the following conditions holds: there exist with such that (2.34) is satisfied for and (2.33) is satisfied for ; there exist with such that (2.33) is satisfied for and (2.34) is satisfied for.
Thus (3.3) is satisfied for m = 1.
there exist, with, such that (2.34) is satisfied for, (2.33) is satisfied for, and (2.34) is satisfied for ; there exist, with and, such that (2.33) is satisfied for, (2.34) is satisfied for, and (2.33) is satisfied for.
If (i) is satisfied for and (ii) is satisfied for, then Lemma 2.4 is still true.
That is, (2.4) is satisfied for (m = 1).
(2.7) Now suppose that (2.4) is satisfied for (kleqq n).
(4.2) Note that condition (2.5) is satisfied for (ale4/3).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com