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The proof of Corollary 2.2 coincides with the proof of the main theorem when (n=1).
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In this section, we only give some examples to illustrate the main theorems when (lambda=0) and (theta=frac{1}{4}).
In this section, we state and prove the main theorem via Galerkin method when is bounded.
The contractive condition of the main theorem is trivial for the case when x = y = 0. Suppose, without any loss of generality, that all x, y are nonzero and x < y.
Let φ ( t ) = 1 5 for all t ∈ P. The contractive condition of the main theorem is trivial for the case when x = y = z = 0. Suppose, without any loss of generality, that all x, y and z are nonzero and x < y < z.
Theorem 3.3 (main theorem).
Example of main theorem.
The main theorem follows.
The following theorem is our main theorem.
This proves our main theorem.
The proof of Main Theorem.
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