Sentence examples for cases for λ from inspiring English sources

Let us consider two possible cases for λ.

One can see that Halley's method and super-Halley's method are the special cases for λ = 1 2 and λ = 1.

In particular, we examine the following cases for the λ i, parameters: 1.

Theorem 3.4 includes the case that for λ close to λ k + 1 A from the right-hand side, the linking with respect to E k + 1 ⊕ E k + 1 ⊥ is constructed provided the negative values of F are small.

Example 3.5 We examine system (3.1) on [ 0, ∞ ) Z with the particular choice of λ 0 ∈ C ∖ R. We will show that system (3.1) with λ = λ 0 is in the limit point case, so that by [[1], Corollary 4.19] it is in the limit point case for every λ ∈ C ∖ R. Let λ 0 = 2 + i 2 3, i.e., system (3.1) reduces to the second-order difference equation x k + 2 + i 2 3 x k + 1 + x k = 0 on [ 0, ∞ ) Z.

This may not be the case for {λ t }, but it is convenient to force this property by assuming boldsymbol{lambda}_{t+1} = mathcal{P}[boldsymbol{lambda}_{t} + boldsymbol{E}_{t} (boldsymbol{A} boldsymbol{x}_{t+1}-boldsymbol{z}_{t+1})] (26).

In recent years, [14] and [15] considered some Hilbert-type operators relating (1 - 3); [16] also considered a multiple Hilbert-type integral operator with the homogeneous kernel of − n + 1 -degree and the relating particular case of (5) (for λ = n − 1, 1 r i = 1 n − 1 ( 1 − 1 p i ) ).

For the case of λ < a, it is obviously that u = 0 is locally asymptotically stable.

The Hyers-Ulam stability for the case of λ = 1 was excluded in Corollary 3.4.

The generalized Hyers-Ulam stability problem for the case of λ = 1 was excluded in Corollary 3.4.

For the case of λ < μ + α, it is obvious that u = 0 is locally asymptotically stable.