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Hence, this yields the uniqueness of the fixed point.

The Banach contraction mapping principle yields the uniqueness of positive solution to BVP (1.1).

Lemma 2.2 yields the uniqueness of classical solutions of problem (2.1 - 2.3 2.1 - 2.3

This yields the uniqueness of the solution of problems (12), (17), and (18).

Finally, the totality in Γ of elements ((1-{J}^z )^{-otimes1}) with any ({zinmathcal{Q}}) yields the uniqueness of these representations.

Our fixed point results do not guarantee the uniqueness of fixed points, however, an appropriate application of condition (6) of Theorem 1 yields the uniqueness of fixed points.

Proof We start proving estimate (3.4) that yields also to the uniqueness of the solution at once.

This yields the uniqueness statement.

The uniqueness of (N) yields (N=O_{p}(G)).

Finally, the uniqueness of the limit yields the desired result.

The uniqueness of the limit yields (z=Tz).