CONVERGENT PROBLEM OF ITERATIVE SEQUENCES FOR NONLINEAR MAPPINGS WITH ERROR MEMBERS IN BANACH SPACES

In this paper,the approximation problems of Ishikawa iteration with errors of fixed points for asymptotically nonexpansive mappings and asymptotically pseudocontractive mappings in arbitrary real Banach spaces are investigated.Some necessary condition and sufficient condition for the convergence of iterative sequences are given respectively.The results thus extend and improve some recent corresponding results.

CONVERGENCE OF ISHIKAWA TYPE ITERATIVE SEQUENCE WITH ERRORS FOR QUASI-CONTRACTIVE MAPPINGS IN CONVEX METRIC SPACES

Some convergence theorems of Ishikawa type iterative sequence with errors for nonlinear general quasi-contractive mapping in convex metric spaces are proved. The results not only extend and improve the corresponding results of L. B. Ciric, Q. H. Liu, H. E. Rhoades and H. K. Xu, et al., but also give an affirmative answer to the open question of Rhoades-Naimpally- Singh in convex metric spaces.

ISHIKAWA TYPE ITERATIVE SEQUENCES WITH ERRORS FOR LIPSCHITZIAN φ-STRONGLY ACCRETIVE OPERATOR EQUATIONS IN ARBITRARY BANACH SPACES

In this paper, we investigate the problem of approximating solutions of the equations of Lipschitzian ψ-strongly accretive operators and fixed points of Lipschitzian ψ-hemicontractive operators by lshikawa type iterative sequences with errors. Our results unify, improve and extend the results obtained previously by several authors including Li and Liu (Acta Math. Sinica 41 (4)(1998), 845-850), and Osilike (Nonlinear Anal. TMA, 36(1)(1999), 1-9), and also answer completely the open problems mentioned by Chidume (J. Math. Anal. Appl. 151 (2)(1990), 453-461).

SOME CONVERGENCE PROBLEM OF ITERATIVE SEQUENCESFOR ACCRETIVE AND PSEUDO-CONTRACTIVETYPE MAPPING IN BANACH SPACES

Some necessary and sufficient conditions for convergence of Ishikawa Mann and steepest descent iterative sequence for accretive and pseudo-contractive type mapping in Banach spaces were obtained. The results improve, extend and include some recent results.

A Monotonicity Condition for Strong Convergence of the Mann Iterative Sequence for Demicontractive Maps in Hilbert Spaces

Let?be a real Hilbert space and?C?be a nonempty closed convex subset of H. Let T : C?→?C?be a demicontractive map satisfying?〈Tx, x〉?≥?‖x‖2 for all?x?∈ D (T). Then the Mann iterative sequence given by?xn + 1?= (1 - an) xn +?anT xn, where an ∈?(0, 1) n?≥?0, converges strongly to an element of F (T):= {x?∈ C : Tx = x}. This strong convergence is obtained without the compactness-type assumptions on C, which many previous results (see e.g. [1]) employed.

Convergence of Iterative Sequence with Mixed Errors for Uniformly Quasi-Lipschitzian Mappings

In convex metric spaces, the sufficient and necessary conditions for Ishikawa iterative sequences of uniformly quasi-Lipschitzian mapping T with mixed errors to converge to a fixed point ate proved, and as a special case, in which T need not be continuous. The results of this paper improve and extend some recent results.

Fundamental Trackability Problems for Iterative Learning Control

Generally, the classic iterative learning control(ILC)methods focus on finding design conditions for repetitive systems to achieve the perfect tracking of any specified trajectory,whereas they ignore a fundamental problem of ILC: whether the specified trajectory is trackable, or equivalently, whether there exist some inputs for the repetitive systems under consideration to generate the specified trajectory? The current paper contributes to dealing with this problem. Not only is a concept of trackability introduced formally for any specified trajectory in ILC, but also some related trackability criteria are established. Further, the relation between the trackability and the perfect tracking tasks for ILC is bridged, based on which a new convergence analysis approach is developed for ILC by leveraging properties of a functional Cauchy sequence(FCS). Simulation examples are given to verify the effectiveness of the presented trackability criteria and FCS-induced convergence analysis method for ILC.

Using Walsh-m Composite Sequence and LDPC-QPSK Joint Iteration to Reduce ISI in Long-range Underwater Acoustic Systems

To reduce inter-symbol-interference (ISI) in underwater acoustic (UWA) communication systems, a method based on LDPC-QPSK joint iteration and Walsh-m composite sequence is proposed in this paper. The method is intended for use in long-range and low signal-to-noise ratio (SNR) UWA communications. At the transmitter, Walsh-m composite sequence is introduced to resist multipath effect. At the receiver, a soft-input soft-output (SISO) module is implemented in a joint iterative process between QPSK demodulator and LDPC decoder. This method is demonstrated in three types of UWA channel models: positive, negative and invariable sound velocity gradients channels. It is shown that through contrastive simulation experiments, this method is more efficient than conventional methods based on independent decoding and demodulation. After two rounds of joint iteration, the proposed method can obtain 2.5 dB over conventional method at BER of 10-5. Numerical results verify that the proposed method is a good candidate for long-range underwater acoustic communication systems.

Hepatic MR imaging using IDEAL-IQ sequence:Will Gd-EOB-DTPA interfere with reproductivity of fat fraction quantification?

BACKGROUND Iterative decomposition of water and fat with echo asymmetry and least squares estimation quantification sequence(IDEAL-IQ)is based on chemical shift-based water and fat separation technique to get proton density fat fraction.Multiple studies have shown that using IDEAL-IQ to test the stability and repeatability of liver fat is acceptable and has high accuracy.AIM To explore whether Gadoxetate Disodium(Gd-EOB-DTPA)interferes with the measurement of the hepatic fat content quantified with the IDEAL-IQ and to evaluate the robustness of this technique.METHODS IDEAL-IQ was used to quantify the liver fat content at 3.0T in 65 patients injected with Gd-EOB-DTPA contrast.After injection,IDEAL-IQ was estimated four times,and the fat fraction(FF)and R2* were measured at the following time points:Precontrast,between the portal phase(70 s)and the late phase(180 s),the delayed phase(5 min)and the hepatobiliary phase(20 min).One-way repeated-measures analysis was conducted to evaluate the difference in the FFs between the four time points.Bland-Altman plots were adopted to assess the FF changes before and after injection of the contrast agent.P<0.05 was considered statistically significant.RESULTS The assessment of the FF at the four time points in the liver,spleen and spine showed no significant differences,and the measurements of hepatic FF yielded good consistency between T1 and T2[95%confidence interval:-0.6768%,0.6658%],T1 and T3(-0.3900%,0.3178%),and T1 and T4(-0.3750%,0.2825%).R2* of the liver,spleen and spine increased significantly after injection(P<0.0001).CONCLUSION Using the IDEAL-IQ sequence to measure the FF,we can obtain results that will not be affected by Gd-EOB-DTPA.The high reproducibility of the IDEAL-IQ sequence makes it available in the scanning interval to save time during multiphase examinations.

The Law of the Iterated Logarithm for the Sums of φ-Mixing Sequences with Duple Suffixes

Hu Shuhe gets a sufficient condition on the law of the iterated logarithm for the sums of φ-mixing sequences with duple suffixes. This paper greatly improves his condition.

ON THE ITERATIVE APPROXIMATION PROBLEM OF FIXED OINTS FOR ASYMPTOTICALLY NON-EXPANSIVE TYPE MAPPINGS IN BANACH SPACES

Some iterative approximation theorems of fixed points for asymptotically nonexpansive type mappings in Banach spaces are obtained.

MANN AND ISHIKAWA ITERATIVE APPROXIMATION OF SOLUTIONS FOR m-ACCRETIVE OPERATOR EQUATIONS

The purpose of this paper is to study the Mann and Ishikawa iterative approximation of solutions for m_accretive operator equations in Banach spaces. The results presented in this paper extend and improve some authors' recent results.

A Hybrid Estimation of Distribution Algorithm for Unrelated Parallel Machine Scheduling with Sequence-Dependent Setup Times

A hybrid estimation of distribution algorithm (EDA) with iterated greedy (IG) search (EDA-IG) is proposed for solving the unrelated parallel machine scheduling problem with sequence-dependent setup times (UPMSP-SDST). For makespan criterion, some properties about neighborhood search operators to avoid invalid search are derived. A probability model based on neighbor relations of jobs is built in the EDA-based exploration phase to generate new solutions by sampling the promising search region. Two types of deconstruction and reconstruction as well as an IG search are designed in the IG-based exploitation phase. Computational complexity of the algorithm is analyzed, and the effect of parameters is investigated by using the Taguchi method of design-of-experiment. Numerical tests on 1640 benchmark instances are carried out. The results and comparisons demonstrate the effectiveness of the EDA-IG. Especially, the bestknown solutions of 531 instances are updated. In addition, the effectiveness of the properties is also demonstrated by numerical comparisons. © 2014 Chinese Association of Automation.

ITERATIVE PROCESS FOR CERTAIN NONLINEAR MAPPINGS WITH LIPSCHITZ CONDITION

Using the new analysis techniques, the problem of iterative approximation of solutions of the equation for Lipschitz phi-strongly accretive operators and of fixed points for Lipschitz phi-strongly pseudo-contractive mappings are discussed. The main results of this paper improve and extend the corresponding results obtained by Chang, Chidume, Deng, Ding, Tan-Xu and Osilike.

ITERATIVE PROCESS TO -HEMICONTRACTIVE OPERATOR AND-STRONGLY ACCRETIVE OPERATOR EQUATIONS

Let E be an arbitrary real Banach space and K be a nonempty closed convex subsets of E. Let T:K→K be a uniformly continuous _hemicontractive operator with bounded range and a n,b n,c n,a ′ n,b ′ n,c ′ n be sequences in [0,1] satisfying:ⅰ) a n+b n+c n=a ′ n+b ′ n+c ′ n=1. n≥0; ⅱ) lim b n= lim b ′ n= lim c ′ n= 0; ⅲ)∑∞n=0b n=∞; ⅳ) c n=o(b n). For any given x 0,u 0,v 0∈K, define the Ishikawa type iterative sequence x n as follows: x n+1 =a nx n+b nTy n+c nu n, y n=a ′ nx n+b ′ nTx n+c ′ nv n (n≥0), where u n and v n are bounded sequences in K. Then x n converges strongly to the unique fixed point of T. Related result deals with the convergence of Ishikawa type iterative sequence to the solution of _strongly accretive operator equations.

CONVERGENCE OF IMPLICIT ITERATIVE PROCESS WITH ERRORS FOR A FINITE FAMILY OF ASYMPTOTICALLY NONEXPANSIVE MAPPINGS

The purpose of this article is to study the weak and strong convergence of implicit iteration process with errors to a common fixed point for a finite family of asymptotically nonexpansive mappings and nonexpansive mappings in Banach spaces. The results presented in this article extend and improve the corresponding results of [1, 2, 4-9, 11-15].

ISHIKAWA ITERATIVE PROCESS FOR CONSTRUCTING SOLUTIONS OF m-ACCRETIVE OPERATOR EQUATIONS

The convergence of the Ishikawa iteration sequences with errors for constructing solutions of m-accretive operator equations is characterized. Moreover, the error estimates of approximate solutions for locally Lipschitzian and m-accretive operator equations are established.

Strong Convergence Results for Hierarchical Circularly Iterative Method about Hierarchical Circularly Optimization

An hierarchical circularly iterative method is introduced for solving a system of variational circularly inequalities with set of fixed points of strongly quasi-nonexpansive mapping problems in this paper. Under some suitable conditions, strong convergence results for the hierarchical circularly iterative sequence are proved in the setting of Hilbert spaces. Our scheme can be regarded as a more general variant of the algorithm proposed by Maingé.

Iterative Technology in a Singular Fractional Boundary Value Problem with q -Difference

In this paper, we apply the iterative technology to establish the existence of solutions for a fractional boundary value problem with q-difference. Explicit iterative sequences are given to approxinate the solutions and the error estimations are also given.

Adding Pseudo-Random Test Sequence Generator in the Test Simulator for DFT Approach

This paper presents modified version of a realistic test tool suitable to Design For Testability （DFT） and Built-ln Self Test （BIST） environments. A comprehensive tool is developed in the form of a test simulator. The simulator is capable of providing a required goal of test for the Circuit Under Test （CUT）. The simulator uses the approach of fault diagnostics with fault grading procedures to provide the optimum tests. The current version of the simulator embeds features of exhaustive and pseudo-random test generation schemes along with the search solutions of cost effective test goals. The simulator provides facilities of realizing all possible pseudo-random sequence generators with all possible combinations of seeds. The tool is developed on a common Personal Computer （PC） platform and hence no special software is required. Thereby, it is a low cost tool hence economical. The tool is very much suitable for determining realistic test sequences for a targeted goal of testing for any CUT. The developed tool incorporates flexible Graphical User Interface （GUI） procedures and can be operated without any special programming skill. The tool is debugged and tested with the results of many bench mark circuits. Further, this developed tool can be utilized for educational purposes for many courses such as fault-tolerant computing, fault diagnosis, digital electronics, and safe-reliable-testable digital logic designs.