convergence analysis of implicit iterative algorithms for asymptotically nonexpansive mappings in this paper we consider the weak and strong convergence of an implicit iterative process with errors for two finite families of asymptotically nonexpansive mappings in the framework of banach spaces our results presented in this paper improve and extend the recent ones announced by many others

convergence of the new composite implicit iteration process with random errors abstract in this paper strong convergence theorems for approximation of common fixed points of a finite family of asymptotically demicontractive mappings are proved in banach spaces using the new composite implicit iteration scheme with errors our results of this paper improve and extend the corresponding results of chen song zhou r d chen y s song h y zhou convergence theorems for implicit iteration process for a finite family of continuous pseudocontractive mappings j math anal appl 314 2006 701 709 osilike m o osilike implicit iteration process for common fixed points of a finite family of strictly pseudocontractive maps j math anal appl 294 2004 73 81 gu f gu the new composite implicit iterative process with errors for common fixed points of a finite family of strictly pseudocontractive mappings j math anal appl 329 2007 766 776 and yang and hu l p yang g hu convergence of implicit iteration process with random errors acta math sinica chin ser 51 1 2008 11 22

structural modeling and psychometrika an historical perspective on growth and achievements the field of linear structural equation modeling with continuous variables is reviewed trends in psychometric theory and data analysis across the five decades of publication ofpsychometrika are discussed especially the clarification of concepts of population and sample explication of the parametric structure of models delineation of concepts of exploratory and confirmatory data analysis expansion of statistical theory in psychometrics estimation via optimization of an explicit objective function and implementation of general function minimization methods developments in the ideas of factor analysis latent variables as well as structural and causal modeling are noted some major conceptual achievements involving general covariance structure representations multiple population models and moment structures are reviewed the major statistical achievements of normal theory generalized least squares estimation elliptical and distribution free estimation and higher moment estimation are discussed computer programs that implement some of the theoretical developments are described

a new iteration process for finite families of generalized lipschitz pseudo contractive and generalized lipschitz accretive mappings abstract a new iteration process is introduced and proved to converge strongly to a common fixed point for a finite family of generalized lipschitz nonlinear mappings in a real reflexive banach space e with a uniformly g teaux differentiable norm if at least one member of the family is pseudo contractive it is also proved that a slight modification of the process converges to a common zero for a finite family of generalized lipschitz accretive operators defined on e results for nonexpansive families are obtained as easy corollaries finally the new iteration process and the method of proof are of independent interest

convergence theorems for common fixed points for finite families of nonexpansive mappings in reflexive banach spaces let e be a real reflexive banach space with a uniformly g teaux differentiable norm let k be a nonempty closed convex subset of e suppose that every nonempty closed convex bounded subset of k has the fixed point property for nonexpansive mappings let t1 t2 tn be a family of nonexpansive self mappings of k with f i 1nfix ti 0 f fix tntn 1 t1 fix t1tn t2 fix tn 1tn 2 t1tn let n be a sequence in 0 1 satisfying the following conditions c1 lim n 0 c2 n for a fixed 0 1 define sn k k by snx 1 x tnx x k where tn tnmodn for an arbitrary fixed u x0 k let b x k tntn 1 t1x x 1 u for some 1 be bounded and let the sequence xn be defined iteratively by xn 1 n 1u 1 n 1 sn 1xn for n 0 assume that limn tnxn tn 1xn 0 then xn converges strongly to a common fixed point of the family t1 t2 tn this convergence theorem is also proved for non self maps

weak and strong convergence of composite implicit iteration process in the present paper we propose a modified composite implicit iteration process for finite family of asymptotically nonexpansive mappings and prove some weak and strong convergence theorems for this family of mappings using proposed iteration process our results extend and generalize some well known results

bootstrap critical values for testing homogeneity of covariance matrices abstract bartlett s modified likelihood ratio statistic a is often suggested in multivariate analysis for testing equality of covariance matrices unfortunately the 2 approximation to the null distribution of 2 log is useful only when the data is normally distributed this article presents a pooled bootstrap procedure that replaces the 2 approximation and makes bartlett s statistic a useful tool for data analysis this procedure also applies to most quadratic form test statistics

analysis of dynamic crack propagation using a time domain boundary integral equation method abstract presented in this paper is a boundary element method which enables the simulation of dynamic crack propagation under arbitrary loading conditions and without any a priori assumptions regarding the crack path the direction and speed of crack advance are controlled only by a fracture criterion fast crack growth is investigated in an unbounded linear elastic body under plane strain or longitudinal shear for in plane deformation under mixed mode loading the influence of crack closure on the computed crack path is considered by solving the related contact problem the starting point is a non hypersingular time domain traction boundary integral equation a collocation method in conjunction with a time stepping scheme is applied to solve the integral equation numerically the accuracy of the numerical method is checked by comparison with analytical solutions available for simple situations some examples of curved cracks propagating with variable speed in inhomogenous stress fields serve to illustrate the versatility of the method

convergence of an implicit iterative process for asymptotically pseudocontractive nonself mappings abstract in this work an implicit iterative process is considered for asymptotically pseudocontractive nonself mappings weak and strong convergence theorems for common fixed points of a family of asymptotically pseudocontractive nonself mappings are established in the framework of hilbert spaces

multilevel analysis of structural equation models summary this paper considers the multilevel analysis of structural equation models with unbalanced sampling designs the analysis is based on the maximum likelihood and the generalized least squares approaches basic statistical results for inference such as the asymptotic distribution of the estimators goodness of fit test statistics for the validity of the model and functional constraints are developed computationally the applications of the scoring algorithm and the gauss newton algorithm are discussed

on the convergence of implicit iteration process with error for a finite family of asymptotically nonexpansive mappings abstract the purpose of this paper 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 paper extend and improve the corresponding results of h bauschke the approximation of fixed points of compositions of nonexpansive mappings in hilbert space j math anal appl 202 1996 150 159 b halpern fixed points of nonexpansive maps bull amer math soc 73 1967 957 961 p l lions approximation de points fixes de contractions c r acad sci paris ser a 284 1977 1357 1359 s reich strong convergence theorems for resolvents of accretive operators in banach spaces j math anal appl 75 1980 287 292 z h sun strong convergence of an implicit iteration process for a finite family of asymptotically quasi nonexpansive mappings j math anal appl 286 2003 351 358 r wittmann approximation of fixed points of nonexpansive mappings arch math 58 1992 486 491 h k xu m g ori an implicit iterative process for nonexpansive mappings numer funct anal optimiz 22 2001 767 773 y y zhou s s chang convergence of implicit iterative process for a finite family of asymptotically nonexpansive mappings in banach spaces numer funct anal optimiz 23 2002 911 921

strong convergence of an implicit iteration process for a finite family of asymptotically quasi nonexpansive mappings in the present paper we prove that the modified implicit iteration sequence for a finite family of asymptotically quasi nonexpansive mappings converges strongly to a common fixed point of the family in a uniformly convex banach space requiring one member t in the family to be semi compact our results extend and improve some recent results

some convergence theorems of non implicit iteration process with errors for a finite families of i asymptotically nonexpansive mappings the purpose of this paper is to study the weak and strong convergence of non implicit iteration process with errors to a common fixed point for a finite family of i asymptotically quasi nonexpansive mappings in banach spaces the results presented in this paper extend and improve the corresponding results of several authors 1 2 7 14 17 19 22 29

using phantom and imaginary latent variables to parameterize constraints in linear structural models the most widely used computer programs for structural equation models analysis are the lisrel series of joreskog and sorbom the only types of constraints which may be made directly are fixing parameters at a constant value and constraining parameters to be equal rindskopf 1983 showed how these simple properties could be used to represent models with more complicated constraints namely inequality constraints on unique variances in this paper two new concepts are introduced which enable a much wider variety of constraints to be made the concepts phantom and imaginary latent variables allow fairly general equality and inequality constraints on factor loadings and structural model coefficients

fixed point solutions of variational inequalities for a finite family of asymptotically nonexpansive mappings without common fixed point assumption let e be a real banach space with a uniformly gateaux differentiable norm and which possesses uniform normal structure k a nonempty bounded closed convex subset of e t i i 1 n a finite family of asymptotically nonexpansive self mappings on k with common sequence k n n 1 1 t n s n be two sequences in 0 1 such that s n t n 1 n 1 and f be a contraction on k under suitable conditions on the sequences s n t n we show the existence of a sequence x n satisfying the relation x n 1 1k n x n s nk nf x n t nk nt r n nx n where n l nn r n for some unique integers l n 0 and 1 r n n further we prove that x n converges strongly to a common fixed point of t i i 1 n which solves some variational inequality provided x n t ix n 0 as n for i 1 2 n as an application we prove that the iterative process defined by z 0 k z n 1 1 1k n z n s nk nf z n t nk nt r n nz n converges strongly to the same common fixed point of t i i 1 n

the viscosity approximation method for asymptotically nonexpansive mappings in banach spaces abstract a recent trend in the iterative methods for constructing fixed points of nonlinear mappings is to use the viscosity approximation technique the advantage of this technique is that one can find a particular solution to the associated problems and in most cases this particular solution solves some variational inequality in this paper we try to extend this technique to find a particular common fixed point of a finite family of asymptotically nonexpansive mappings in a banach space which is reflexive and has a weakly continuous duality map both implicit and explicit viscosity approximation schemes are proposed and their strong convergence to a solution to a variational inequality is proved

explicit averaging cyclic algorithm for common fixed points of asymptotically strictly pseudocontractive maps weak and strong convergence theorems for the approximation of common fixed points of a finite family of asymptotically strictly pseudocontractive mappings are proved in hilbert spaces using an explicit averaging cyclic algorithm

the equivalence of the convergence of four kinds of iterations for a finite family of uniformly asymptotically o pseudocontractive mappings in this paper we prove the equivalences of the strong convergence each other the modified mann iterative process with errors the modified ishikawa iterative process with errors the implicit iterative process with errors and the composite implicit iterative process with errors for a finite family of uniformly asymptotically o pseudocontractive mappings in arbitrary real banach space the results presented in this paper generalize and improve the corresponding results of roades soltuz and huang

weak and strong convergence of the ishikawa iterative process for a finite family of asymptotically nonexpansive mappings abstract in this paper we introduce an ishikawa implicit iterative process with errors for a finite family of n asymptotically nonexpansive mappings as follows x n 1 n n x n 1 n t i n k n y n n u n y n 1 n n x n n t i n k n x n n v n n 1 where for any n n fixed k n 1 denotes the quotient of the division of n by n and i n the rest i e n k n 1 n i n i n 1 n the sequences n n n n are four real sequences in 0 1 satisfying n n 1 and n n 1 for all n 1 un vn are two bounded sequences and x0 is a given point in the setting of uniformly convex banach spaces we give some results of weak and strong convergence of the above iterative process the results presented here are situated on the line of research of the corresponding results of sun j math anal appl 286 1 2003 351 358 osilike j math anal appl 294 1 2004 73 81 chang et al j math anal appl 313 1 2006 273 283 gu j math anal appl 329 2 2007 766 776 huang and noor appl math comput 190 1 2007 356 361 su and qin appl math comput 186 1 2007 271 278 zhou et al appl math comput 173 1 2006 196 212 and some others

on testing functional constraints in structural equation models summary in the context of a robust generalized least squares approach a new statistic for testing the validity of constraints in structural equation models is proposed it is shown that the new test requires significantly less computational effort than the traditional one extension to models in several populations is also considered illustrative applications based on real data are given

covariance structure analysis in several populations this paper is concerned with the study of covariance structural models in several populations estimation theory of the parameters that are subject to general functional restraints is developed based on the generalized least squares approach asymptotic properties of the constrained estimator are studied and asymptotic chi square tests are presented to evaluate appropriate model comparisons the method of multipliers and the standard reparametrization technique are discussed in obtaining the estimates the methodology is demonstrated by a set of real data

approximation of common fixed points for finite families of total asymptotically nonexpansive mappings abstract let e be a real banach space k a closed convex nonempty subset of e let t 1 t 2 t m k k be m total asymptotically nonexpansive mappings an iterative sequence for approximation of common fixed points assuming existence of t 1 t 2 t m is constructed necessary and sufficient conditions for the convergence of the scheme to a common fixed point of the mappings are given furthermore in the case that e is uniformly convex a sufficient condition for convergence of the iteration process to a common fixed point of mappings under our setting is established

alternative test criteria in covariance structure analysis a unified approach in the context of covariance structure analysis a unified approach to the asymptotic theory of alternative test criteria for testing parametric restrictions is provided the discussion develops within a general framework that distinguishes whether or not the fitting function is asymptotically optimal and allows the null and alternative hypothesis to be only approximations of the true model also the equivalent of the information matrix and the asymptotic covariance matrix of the vector of summary statistics are allowed to be singular when the fitting function is not asymptotically optimal test statistics which have asymptotically a chi square distribution are developed as a natural generalization of more classical ones issues relevant for power analysis and the asymptotic theory of a testing related statistic are also investigated

simultaneous equation systems as moment structure models with an introduction to latent variable models abstract an introduction to latent variable covariance structure models is provided estimation and testing of such models with normal and non normal variables is reviewed and a relatively inexpensive asymptotically distribution free estimator is introduced the traditional econometric simultaneous equation system is reconceptualized as a random vector structural equation model extensions of the model to deal with latent variables and a wider variety of structural phenomena are made via the joreskog keesling wiley lisrel approach and a simpler approach due to bentler and weeks these representation systems are extended via first and second moments about the origin of measured variables explained in terms of the structural coefficients and the moments of explanatory variables citations to further literature are provided

on the convergence theorems of implicit iteration process for a finite family of i asymptotically nonexpansive mappings in this paper we consider the weak and strong convergence of implicit iteration process to a common fixed point of i asymptotically nonexpansive mappings the main results extend to a finite family of i asymptotically nonexpansive mappings in a banach space

latent variable structural equation modeling with categorical data abstract structural equation modeling with latent variables is overviewed for situations involving a mixture of dichotomous ordered polytomous and continuous indicators of latent variables special emphasis is placed on categorical variables models in psychometrics econometrics and biometrics are interrelated via a general model due to muthen limited information least squares estimators and full information estimation are discussed an example is estimated with a model for a four wave longitudinal data set where dichotomous responses are related to each other and a set of independent variables via latent variables with a variance component structure

the approximation of fixed points of compositions of nonexpansive mappings in hilbert space determining fixed points of nonexpansive mappings is a frequent problem in mathematics and physical sciences an algorithm for finding common fixed points of nonexpansive mappings in hilbert space essentially due to halpern is analyzed the main theorem extends wittmann s recent work and partially generalizes a result by lions algorithms of this kind have been applied to the convex feasibility problem