ITERATIVE APPROXIMATION OF FIXED POINTS OF (ASYMPTOTICALLY) NONEXPANSIVE MAPPINGS

Let E be a uniformly convex Banach space which satisfies Opial's condition or has a Frechet differentiable norm,and C be a bounded closed convex subset of E. If T∶C→C is (asymptotically)nonexpansive,then the modified Ishikawa iteration process defined byx n+1 =t nT ns nT nx n+1-s nx n+(1-t n)x n,converges weakly to a fixed point of T ,where {t n} and {s n} are sequences in [0,1] with some restrictions.

ON THE CONVERGENCE PROBLEMS OF ISHIKAWA AND MANN ITERATIVE PROCESSES WITH ERROR FOR Φ-PSEUDO CONTRACTIVE TYPE MAPPINGS

The purpose of this paper is to introduce the concept of Φ_pseudo contractive type mapping and to study the convergence problem of Ishikawa and Mann iterative processes with error for this kind of mappings. The results presented in this paper improve and extend many authors'recent results.

ISHIKAWA ITERATIVE PROCESS IN UNIFORMLY SMOOTH BANACH SPACES

Let E be a uniformly smooth Banach space, K be a nonempty closed convex subset of E, and suppose: T: K --> K is a continuous Phi-strongly pseudocontractive operator with a bounded range. Using a new analytical method, under general cases, the Ishikawa iterative process {x(n)} converges strongly to the unique fixed point x* of the operator T were proved. The paper generalizes and extends a lot of recent corresponding results.

Iterative Processes with Errors for Generalized Set-Valued φ-Hemi-contractive Mapping in Banach Spaces

A new conception of generalized set-valued Ф-hemi-contractive mapping in Banach spaces is presented. Some strong convergence theorems of Ishikawa and Mann iterative approximation with errors is proved. The results in this paper improve and extend the earlier results.

Iterative Approximation with Errors for Generalized Set-Valued Strongly Accretive Mapping in Banach Spaces

A new concept of generalized set-valued strongly accretive mappings in Banach spaces was given and some strong convergence theorems of Ishikawa and Mann iterative process with errors approximation methods by Huang et al. was proved. The results presented in this paper improve and extend the earlier results obtained by Huang et al.

Mesh‑free semi‑quantitative variance underestimation elimination method in Monte Caro algorithm

The inter-cycle correlation of fission source distributions(FSDs)in the Monte Carlo power iteration process results in variance underestimation of tallied physical quantities,especially in large local tallies.This study provides a mesh-free semiquantitative variance underestimation elimination method to obtain a credible confidence interval for the tallied results.This method comprises two procedures:Estimation and Elimination.The FSD inter-cycle correlation length is estimated in the Estimation procedure using the Sliced Wasserstein distance algorithm.The batch method was then used in the elimination procedure.The FSD inter-cycle correlation length was proved to be the optimum batch length to eliminate the variance underestimation problem.We exemplified this method using the OECD sphere array model and 3D PWR BEAVRS model.The results showed that the average variance underestimation ratios of local tallies declined from 37 to 87%to within±5%in these models.

A novel three-step implicit iteration process for threeΦ-hemicontractive mapping in the intermediate sense

In this paper,we introduce a three-step composite implicit iteration process for approximating the common fixed point of three uniformly continuous and asymptotically generalizedΦ-hemicontractive mappings in the intermediate sense.We prove that our proposed iteration process converges to the common fixed point of three finite family of asymptotically generalizedΦ-hemicontractive mappings in the intermediate sense.Our results extends,improves and complements several known results in literature.

Carlson iterating rational approximation and performance analysis of fractional operator with arbitrary order

The performance analysis of the generalized Carlson iterating process,which can realize the rational approximation of fractional operator with arbitrary order,is presented in this paper.The reasons why the generalized Carlson iterating function possesses more excellent properties such as self-similarity and exponential symmetry are also explained.K-index,P-index,O-index,and complexity index are introduced to contribute to performance analysis.Considering nine different operational orders and choosing an appropriate rational initial impedance for a certain operational order,these rational approximation impedance functions calculated by the iterating function meet computational rationality,positive reality,and operational validity.Then they are capable of having the operational performance of fractional operators and being physical realization.The approximation performance of the impedance function to the ideal fractional operator and the circuit network complexity are also exhibited.

Convergence Theorems of φ-pseudo Contractive Type Mappings in Normed Linear Spaces

In this paper, by virtue of an inequality and sane analysis techniques, we prove sane convergence theorems cm the iterative process for nonlinear mappings of-pseudo contractive type in named linear spaces, which extend and improve the corresponding results obtained by others recently.

Convergence theorem of common fixed points for Lipschitzian pseudo-contraction semi-groups in Banach spaces

The purpose of this paper is to study the weak convergence problems of the implicity iteration process for Lipschitzian pseudocontractive semi-groups in the general Banach spaces. The results presented in this paper extend and improve the corresponding results of some people.

A Data-Adaptive Filter of the Tahiti-Darwin Southern Oscillation Index and the Associate Scheme of Filling Data Gaps

The Tahiti-Darwin Southern Oscillation index provided by Climate Analysis Center of USA has been used in numerous studies. But, it has some deficiency. It contains noise mainly due to high month-to-month variability. In order to reduce the level of noise in the SO index, this paper introduces a fully data-adaptive filter based on singular spectrum analysis. Another interesting aspect of the filter is that it can be used to fill data gaps of the SO index by an iterative process. Eventually, a noiseless long-period data series without any gaps is obtained.

Picard Approximation of Fixed Points of Nonexpansive Mappings

Let C be a bounded convex subset in a uniformly convex Banach space X, x 0, u n∈C , then x n+1 =S nx n, where S n=α n0 I+α n1 T+α n2 T 2+…+α nk T k+γ nu n, α ni ≥0, 0<α≤α n0 ≤b<1, ∑ki=0α ni +γ n=1, and n≥1. It is proved that x n converges to a fixed point on T if T is a nonexpansive mapping.

APPROXIMATION OF FIXED POINTS OF STRICTLY PSEUDO-CONTRACTIVE MAPPING WITHOUT LIPSCHITZ ASSUMPTION

Without the Lipschitz assumption and boundedness of K in arbitrary Banach spaces, the Ishikawa iteration ｛x n｝ ∞ n=1 defined byx 1∈K,\ x n+1 =(1-α n)x n+α nTy n,\ y n=(1-β n)x n+β nTx n,\ n≥1satisfying 0<α n,β n<1 ,for all n≥1;∑ ∞ n=1 α n=∞;α n→0,β n→0 as n→∞ is proved to converge strongly to the unique fixed point of T ,where T:K→K is a uniformly continuous strictly pseudo\|contractive operator with bounded range.

Mathematical Modeling Algorithms for Creating New Materials with Desired Properties Using Nano-Hierarchical Structures

In the enormous and still poorly mastered gap between the macro level, where well developed continuum theories of continuous media and engineering methods of calculation and design operate, and atomic, subordinate to the laws of quantum mechanics, there is an extensive meso-hierarchical level of the structure of matter. At this level unprecedented previously products and technologies can be artificially created. Nano technology is a qualitatively new strategy in technology: it creates objects in exactly the opposite way—large objects are created from small ones [1]. We have developed a new method for modeling acoustic monitoring of a layered-block elastic medium with several inclusions of various physical and mechanical hierarchical structures [2]. An iterative process is developed for solving the direct problem for the case of three hierarchical inclusions of l, m, s-th ranks based on the use of 2D integro-differential equations. The degree of hierarchy of inclusions is determined by the values of their ranks, which may be different, while the first rank is associated with the atomic structure, the following ranks are associated with increasing geometric sizes, which contain inclusions of lower ranks and sizes. Hierarchical inclusions are located in different layers one above the other: the upper one is abnormally plastic, the second is abnormally elastic and the third is abnormally dense. The degree of filling with inclusions of each rank for all three hierarchical inclusions is different. Modeling is carried out from smaller sizes to large inclusions;as a result, it becomes possible to determine the necessary parameters of the formed material from acoustic monitoring data.

THE LOCAL CONTINUITY MODULI FOR TWO CLASSES OF GAUSSIAN PROCESSES

In this article,local continuity moduli for the fractional Wiener process and l ∞\|valued Gaussian processes is discussed.

ON THE INITIAL VALUE PROBLEMS OF FIRST ORDERIMPULSIVE DIFFERENTIAL SYSTEMS

The purpose of this paper is to study the existence and iterative approximation of minimax quasi-solutions for a class of initial value problems of first order impulsive differential systems by using monotone iterative methods.

IPSETFUL： an iterative process of selecting test cases for effective fault localization by exploring concept lattice of program spectra

Fault localization is an important and challeng- ing task during software testing. Among techniques studied in this field, program spectrum based fault localization is a promising approach. To perform spectrum based fault local- ization, a set of test oracles should be provided, and the ef- fectiveness of fault localization depends highly on the quality of test oracles. Moreover, their effectiveness is usually af- fected when multiple simultaneous faults are present. Faced with multiple faults it is difficult for developers to determine when to stop the fault localization process. To address these issues, we propose an iterative fauk localization process, i.e., an iterative process of selecting test cases for effective fault localization （IPSETFUL）, to identify as many faults as pos- sible in the program until the stopping criterion is satisfied. It is performed based on a concept lattice of program spec- trum （CLPS） proposed in our previous work. Based on the labeling approach of CLPS, program statements are catego- rized as dangerous statements, safe statements, and sensitive statements. To identify the faults, developers need to check the dangerous statements. Meantime, developers need to se- lect a set of test cases covering the dangerous or sensitive statements from the original test suite, and a new CLPS is generated for the next iteration. The same process is pro- ceeded in the same way. This iterative process ends until there are no failing tests in the test suite and all statements on the CLPS become safe statements. We conduct an empirical study on several subject programs, and the results show that IPSETFUL can help identify most of the faults in the program with the given test suite. Moreover, it can save much effort in inspecting unfaulty program statements compared with the existing spectrum based fault localization techniques and the relevant state of the art technique.

Weak Convergence Theorem for Lipschizian Pseudocontraction Semigroups in Banach Spaces

The purpose of this paper is to study the weak convergence problems of the irnplicity iteration process for Lipschitzian pseudocontraction semigroups in general Banach spaces. The results presented in this paper extend and improve the corresponding results of Zhou [Nonlinear Anal., 68, 2977-2983 （2008）], Chen, et ah [J. Math. Anal. Appl., 314, 701 709 （2006）], Xu and Ori [Numer. Funct. Anal. Optim, 22, 767-773 （2001）] and Osilike [J. Math. Anal. Appl., 294, 73-81 （2004）]. Keywords

Three-step Iterations with Errors for Nonlinear Strongly Accretive Operator Equations

In this paper, we suggest and analyse a three-step iterative scheme with errors for solving nonlinear strongly accretive operator equation Tx = f without the Lipshitz condition. The results presented in this paper improve and extend current results in the more general setting.

An Implicit Iteration Process with Errors for a Finite Family of r-strictly Asymptotically Pseudocontractive Mappings

In this paper, we will establish several strong convergence theorems for the approximation of common fixed points of r-strictly asymptotically pseudocontractive mappings in uniformly convex Banach spaces using the modiied implicit iteration sequence with errors, and prove the necessary and sufficient conditions for the convergence of the sequence. Our results generalize, extend and improve the recent work, in this topic.