... state Theorem 2.13 to give a sufficient condition to have convergence of the
vectorial continued fraction 1.1.
A similar theorem was given by Peng and Hessel 5, to study convergence of the
vectorial ... Fair 1 for vectorial continued fractions according to the norm
convergence.
Theorem 2.5. Let a
n
e, for all n ≥ 1,andb
n
be a sequence of commuting...
... α
n
S
r
z
n
,n≥ 0. 3.14
We need the strong convergence of the implicit algorithm 1.17 to prove the strong
convergence of the explicit algorithm 3.14.
Theorem 3.2. Let E be a strictly convex ... our main results, we also need the following lemmas.
The first part of the next lemma is an immediate consequence of the subdifferential
inequality, and the proof...
... in the fixed point set of a strict
pseudocontraction and in the zero set of a nonlinear mapping which is the sum of a maximal
monotone operator and an inverse strongly monotone mapping. Strong convergence ... pseudocontraction and in the zero set of a
nonlinear mapping which is the sum of a maximal monotone operator and a inverse strongly
monotone mapping. Strong converg...
... the result of Morales and Jung 15 from
continuous pseudocontractions to demicontinuous pseudocontractions in the framework of
Hilbert spaces. To be more precise, they proved the following theorem.
Theorem ... said to be monotone if
Ax − Ay, x − y
≥ 0, ∀x, y ∈ C. 1.1
2 The single-valued mapping A : C → H is maximal if the graph GA of A is not
properly containe...
... weakly to
an element of FT. This completes the proof.
References
1 K. Goebel and W. A. Kirk, “A fixed point theorem for asymptotically nonexpansive mappings,”
Proceedings of the American Mathematical ... results of Suantai 7 and others for nonself-
mappings and those of Chidume et al. 12 in the sense that our iterative process contains
the one used by them. The conc...
... proof of its
convergence has not been provided yet. In this article we are filling this gap.
The mimetic method for the steady diffusion equations (4.1) is too general for the
purpose of our theoretical ... equation is developed and described.
Then, in Section 5 we present the proof of the quadratic convergence rate of the new
method. Next, the solution and analysis...
... only
considers the quality of the worst link of a path. It does not
explicitly take into account the other characteristics of the
path, such as the hop count or the LQI of the rest of the links.
4.9. ... function of the LQI of the link.
The link cost is an estimate of the number of transmission
attempts required for successful frame delivery in a link...
... completes the proof of the convexity of FT. From the continuity of T,we
can also obtain the closedness of FT. The proof is completed.
Lemma 1.5. Let C be a nonempty close convex subset of a real ... 1, then the class of asymptotically pseudocontractive
mappings in the intermediate sense is reduced to the class of asymptotically pseudocontrac-
tive mappings....
... 2, then 3.1 holds on 0,π/4 and 1.8
holds.
4. The Special Cases of Theorems 1.5 and 1.6
1 Taking a 3,b
1
a − 1 2 in Theorem 1.5 and c 6,d
1
c − 2 4 in Theorem 1.6
leads to the ... hen the functions fx −
fb/gx − gb and fx − fa/gx − ga are also i ncreasing (or decreasing) on a, b.
3. Proofs of Theorems 1.5 and 1.6
A We first process the...
... but the
variation of the level and the level differences between the
microphones are much stronger. The results of the in-ear
measurements show a raise of 10 dB to 15 dB in comparison
to the theoretical ... for the microphone
positions corresponding to the entrances of the ear canals
of the HATS and the positions of the BTE hearing aid
microphones on...