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Remark 3.2 There are some fixed point theorems, which involve several operators such as the operators T x : = A x + B x in a Banach space, or T x : = A x B x + C x in Banach algebras etc., and they may be formulated by Theorem 3.1 in a coincident form.

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From the above definitions, we note that the class of demicontractive operators contains important operators such as the directed operators, the quasi-nonexpansive operators and the strictly pseudo-contractive operators with fixed points.

From the above definitions, we note that the class of demicontractive operators contains important operators such as the directed operators, the quasi-nonexpansive operators and the strictly pseudocontractive mappings with fixed points.

Therefore, in order to improve the overall throughput performance, we propose to adjust the utility functions of operators depending on the spectrum usage status such as the operator payoff, the amount of unused spectrum, and the amount of spectrum loss caused by signal collisions.

If a partial differential operator is of splitting rank 2, such as the operator associated with Poisson or Helmholtz, the corresponding PDE is solved via a generalized Sylvester matrix equation, and a bivariate polynomial approximation of the solution of degree (nx,ny) is computed in O((nxny)3/2) operations.

When the patient is too unstable to be moved safely, US is the standard bedside examination but it has disadvantages, such as the operator-dependent results and extensive patient preparation [ 3].

The theory of boundedness of classical operators of the real analysis, such as the maximal operator, fractional maximal operator, Riesz potential and the singular integral operators etc., from one weighted Lebesgue space to another one is well studied.

The main reason for using the Sobel operator is that it is relatively insensitive to noise and it has relatively smaller masks than other operators such as the Roberts operator and the two-order Laplacian operator.

In this section we shall apply Theorems 1-6 of the paper to some particular operators such as the Littlewood-Paley operators, Marcinkiewicz operator and Bochner-Riesz operator.

Either the labels will have to make do with less, or other firms, such as the mobile operators, will have to pitch in.

Potential speedups depend on many design choices such as the search operators, representations and fitness functions used on the islands, and also the parameters of the island model.

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