new bounds for the first inequality of ostrowski gruss type and applications abstract some new bounds for the first inequality of ostrowski gruss type are derived these new bounds can be much better than some recently obtained bounds applications in numerical integration are also given

strong convergence of modified mann iterations abstract the mann iterations for nonexpansive mappings have only weak convergence even in a hilbert space we propose two modifications of the mann iterations in a uniformly smooth banach space one for nonexpansive mappings and the other for the resolvent of accretive operators the two modified mann iterations are proved to have strong convergence

on an iyengar type inequality involving quadratures in n knots abstract in this short note we give an iyengar type inequality involving quadratures in n knots where n is an arbitrary natural number

on sharp inequalities of simpson type and ostrowski type in two independent variables in this paper two sharp inequalities are derived the first is a sharp simpson inequality and the second is a sharp inequality of ostrowski type in two independent variables

strong convergence and certain control conditions for modified mann iteration abstract in this paper we propose a new modified mann iteration for computing fixed points of nonexpansive mappings in a banach space setting this new iterative scheme combines the modified mann iteration introduced by kim and xu t h kim h k xu strong convergence of modified mann iterations nonlinear anal 61 2005 51 60 and the viscosity approximation method introduced by moudafi a moudafi viscosity approximation methods for fixed points problems j math anal appl 241 2000 46 55 we give certain different control conditions for the modified mann iteration strong convergence in a uniformly smooth banach space is established

approximating the finite hilbert transform via a companion of ostrowski s inequality for function of bounded variation and applications the finite hilbert transform plays an important role in scientific and engineering computing by using a companion of ostrowski s inequality for function of bounded variation we give some new approximations of the finite hilbert transform which may have the better error bounds than the known results obtained via ostrowski type inequality some numerical experiments are also presented

convergence theorems of fixed points for κ strict pseudo contractions in hilbert spaces abstract let c be a closed convex subset of a real hilbert space h and assume that t c h is a strict pseudo contraction such that f t x c x t x 0 consider the normal mann s iterative algorithm given by x 1 c x n 1 n x n 1 n p c s x n n 1 where s c h is defined by s x x 1 t x p c is the metric projection of h onto c and n n 1 for all n 1 it is proved that if the control parameter sequence n is chosen so that n 1 and n 1 n 1 n then x n converges weakly to a fixed point of t in order to get a strong convergence theorem we modify the normal mann s iterative algorithm by using a suitable convex combination of a fixed vector and a sequence in c the results presented in this article respectively improve and extend the recent results of marino and xu g marino h k xu weak and strong convergence theorems for strict pseudo contractions in hilbert spaces j math anal appl 329 2007 336 349 from strictly pseudo contractive self mappings to nonself mappings and of kim and xu t h kim h k xu strong convergence of modified mann iterations nonlinear anal 61 2005 51 60 from nonexpansive mappings to strict pseudo contractions

weak and strong convergence theorems for strict pseudo contractions in hilbert spaces abstract let c be a closed convex subset of a real hilbert space h and assume that t is a strict pseudo contraction on c with a fixed point for some 0 1 given an initial guess x 0 c and given also a real sequence n in 0 1 the mann s algorithm generates a sequence x n by the formula x n 1 n x n 1 n t x n n 0 it is proved that if the control sequence n is chosen so that n 1 and n 0 n 1 n then x n converges weakly to a fixed point of t however this convergence is in general not strong we then modify mann s algorithm by applying projections onto suitably constructed closed convex sets to get an algorithm which generates a strong convergent sequence this result extends a recent result of nakajo and takahashi k nakajo w takahashi strong convergence theorems for nonexpansive mappings and nonexpansive semigroups j math anal appl 279 2003 372 379 from nonexpansive mappings to strict pseudo contractions

new error bounds for the simpson s quadrature rule and applications new error bounds for the well known simpson s quadrature rule are derived if we use these bounds then we can apply the simpson s rule to functions whose first second or third derivatives are unbounded below or above furthermore these error bounds can be much better than some recently obtained bounds applications in numerical integration are also given

on the optimal constants of ostrowski like inequalities involving n knots we compute the optimal constants of ostrowski like inequalities involving n knots given by huy and ngo

approximation of a zero point of accretive operator in banach spaces abstract this paper introduces a composite iteration scheme for approximating a zero point of accretive operator in the framework of uniformly smooth banach spaces and the reflexive banach space which has a weak continuous duality map respectively strong convergence of the composite iteration scheme x n defined by y n n x n 1 n j r n x n x n 1 n u 1 n y n where j r n is the resolvent of m accretive operator a and u c is an arbitrary but fixed element in c and sequences n in 0 1 n in 0 1 is established under certain appropriate assumptions on the sequences n n and r n that x n defined by the above iteration scheme converges to a zero point of a is proved the results improve and extend results of t h kim h k xu and some others

a general iterative method for nonexpansive mappings in hilbert spaces let h be a real hilbert space consider on h a nonexpansive mapping t with a fixed point a contraction f with coefficient 0 0 let 0

new results concerning chebyshev gruss type inequalities via discrete oscillations the classical form of gruss inequality was first published by g gruss and gives an estimate of the difference between the integral of the product and the product of the integrals of two functions in the subsequent years many variants of this inequality appeared in the literature the aim of this paper is to consider some new bivariate chebyshev gruss type inequalities via discrete oscillations and to apply them to different tensor products of linear not necessarily positive well known operators we also compare the new inequalities with some older results in the end we give a chebyshev gruss type inequality with discrete oscillations for more than two functions

strong convergence theorems for nonexpansive mappings and inverse strongly monotone mappings abstract in this paper we introduce an iterative scheme for finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality for an inverse strongly monotone mapping in a hilbert space then we show that the sequence converges strongly to a common element of two sets using this result we consider the problem of finding a common fixed point of a nonexpansive mapping and a strictly pseudocontractive mapping and the problem of finding a common element of the set of fixed points of a nonexpansive mapping and the set of zeros of an inverse strongly monotone mapping

identification of confirmatory factor analysis models of different levels of invariance for ordered categorical outcomes this article considers the identification conditions of confirmatory factor analysis cfa models for ordered categorical outcomes with invariance of different types of parameters across groups the current practice of invariance testing is to first identify a model with only configural invariance and then test the invariance of parameters based on this identified baseline model this approach is not optimal because different identification conditions on this baseline model identify the scales of latent continuous responses in different ways once an invariance condition is imposed on a parameter these identification conditions may become restrictions and define statistically non equivalent models leading to different conclusions by analyzing the transformation that leaves the model implied probabilities of response patterns unchanged we give identification conditions for models with invariance of different types of parameters without referring to a specific parametrization of the baseline model tests based on this approach have the advantage that they do not depend on the specific identification condition chosen for the baseline model

a note on some ostrowski like type inequalities abstract error estimate plays an important role for numerical integration some ostrowski like type inequalities concerning a new type of quadrature formula are established recently by huy and ngo 2009 2010 6 7 in this note improvement and extension to these inequalities are given

a generalization of the ostrowski integral inequality for mappings whose derivatives belong to lp a b and applications in numerical integration a generalization of ostrowski integral inequality for mappings whose derivatives belong to l 1 a b and applications for general quadrature formulae are given

improvement of some inequalities of euler gruss type abstract we prove an inequality of gruss type and use it to improve strictly some general euler gruss type inequalities all improved inequalities are sharp

new bounds for moments of continuous random variables in this paper some gruss and ostrowski gruss type inequalities are applied to estimate the moments of continuous random variables whose probability density function is in l p space some results of kumar are generalized p kumar inequalities involving moments of a continuous random variable defined over a finite interval comput math appl 48 2004 257 273 p kumar the ostrowski type moment integral inequalities and moment bounds for continuous random variables comput math appl 49 2005 1929 1940

a general iterative algorithm for nonexpansive mappings in hilbert spaces abstract let h be a real hilbert space suppose that t is a nonexpansive mapping on h with a fixed point f is a contraction on h with coefficient 0 1 and f h h is a k lipschitzian and strongly monotone operator with k 0 0 let 0 2 k 2 0 k 2 2 we proved that the sequence x n generated by the iterative method x n 1 n f x n i n f t x n converges strongly to a fixed point x f i x t which solves the variational inequality f f x x x 0 for x f i x t

a survey on some inequalities for expectation and variance inequalities for continuous random variables having the probability density function defined on a finite interval obtained recently by the authors are surveyed

residual diagnostics for growth mixture models examining the impact of a preventive intervention on multiple trajectories of aggressive behavior growth mixture modeling has become a prominent tool for studying the heterogeneity of developmental trajectories within a population in this article we develop graphical diagnostics to detect misspecification in growth mixture models regarding the number of growth classes growth trajectory means and covariance structures for each model misspecification we propose a different type of empirical bayes residual to quantify the departure our procedure begins by imputing multiple independent sets of growth classes for the sample then from these so called pseudoclass draws we form diagnostic plots to examine the averaged empirical distributions of residuals in each such class our proposals draw on the property that each single set of pseudoclass adjusted residuals is asymptotically normal with known mean and co variance when the underlying model is correct these methods are justified in simulation studies involving two classes of linear growth curves that also differ by their covariance structures

remarks on ostrowski like inequalities abstract we show the error inequalities on quadrature formulas obtained by huy and ngo can be improved if m is even

a general iterative method for equilibrium problems and strict pseudo contractions in hilbert spaces abstract in this paper we introduce two iterative schemes by the general iterative method for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a k strictly pseudo contractive non self mapping in the setting of real hilbert spaces our results improve and extend the corresponding results given by many others

several error inequalities for a quadrature formula with a parameter and applications in this paper we will derive several error inequalities for a quadrature formula with a parameter which will not only provide some generalizations of the known results but also give some other interesting quadrature formulae as special cases furthermore sharp upper and lower error bounds for the double error inequalities are obtained applications in numerical integration are also given

improvement of some ostrowski gruss type inequalities abstract in this paper we improve and further generalize some ostrowski gruss type inequalities involving bounded once and twice differentiable mappings

strong convergence theorems of a general iterative process for a finite family of λi strict pseudo contractions in q uniformly smooth banach spaces in this paper we study a general iterative process to have strong convergence for a finite family of l i strict pseudo contractive non self mappings in the framework of q uniformly smooth banach spaces our results improve and extend the corresponding results announced by many others

some generalized ostrowski gruss type integral inequalities in this paper we establish some new ostrowski gruss type integral inequalities involving k 1 interior points in 1d case which are generalizations of some known results in the literature and one of which is sharp then we deduce an ostrowski gruss type integral inequality in 2d case involving k 1 2 interior points for the first time we also present one application on the estimate of error bound for numerical integration formula in which a sharp error bound for a new numerical integration formula is provided by the results established

a new ostrowski gruss inequality involving 3n knots abstract this is the fifth and last in our series of notes concerning some classical inequalities such as the ostrowski simpson iyengar and ostrowski gruss inequalities in r in the last note we propose an improvement of the ostrowski gruss inequality which involves 3 n knots where n 1 is an arbitrary numbers more precisely suppose that x k k 1 n 0 1 y k k 1 n 0 1 and k k 1 n 0 n are arbitrary sequences with k 1 n k n and k 1 n k x k n 2 the main result of the present paper is to estimate 1 n k 1 n k f a b a y k 1 b a a b f t d t f b f a n k 1 n k y k x k in terms of either f or f unlike the standard ostrowski gruss inequality and its known variants which basically estimate f x a b f t d t b a in terms of a correction term as a linear polynomial of x and some derivatives of f our estimate allows us to freely replace f x and the correction term by using 3 n knots x k k 1 n y k k 1 n and k k 1 n as far as we know this is the first result involving the ostrowski gruss inequality with three sequences of parameters

on some generalizations of an ostrowski gruss type integral inequality in this paper we improve and extend a new ostrowski gruss type integral inequality obtained recently by feng and meng 2012 26 to be precise we show that a condition imposed on the inequality can be removed furthermore we provide a two dimensional generalization of this ostrowski gruss type inequality which is sharp

ostrowski s inequality for vector valued functions and applications abstract in this paper we obtain some ostrowski type inequalities for vector valued functions which both generalise and improve the scalar case and show that the midpoint inequality is the best possible inequality in the class a quadrature formula of the riemann type for the bochner integral and the error bounds are considered applications to operator inequalities and numerical approximation for the mild solution of inhomogeneous vector valued differential equations are also pointed out in the last section a numerical example is analysed

viscosity approximation methods for fixed points problems the aim of this work is to propose viscosity approximation methods which amounts to selecting a particular fixed point of a given nonexpansive self mapping

a note on testing the number of components in a normal mixture in a recent paper lo et al 2001 propose a test for the likelihood ratio statistic based on the kullback leibler information criterion when testing the null hypothesis that a random sample is drawn from a mixture of k 0 normal components against the alternative hypothesis of a mixture with k 1 normal components with k 0 less than k 1 however this result requires conditions that are generally not met when the null hypothesis holds consequently the result is not proven and simulations suggest that it may not be correct

gruss type inequalities abstract a connection between gruss inequality and the error of best approximation is revealed a gruss type inequality that unifies the continuous and discrete versions of the classical gruss inequalities is established

some iterative methods for finding fixed points and for solving constrained convex minimization problems the present paper is divided into two parts in the first part we introduce implicit and explicit iterative schemes for finding the fixed point of a nonexpansive mapping defined on the closed convex subset of a real hilbert space we establish results on the strong convergence of the sequences generated by the proposed schemes to a fixed point of a nonexpansive mapping such a fixed point is also a solution of a variational inequality defined on the set of fixed points in the second part we propose implicit and explicit iterative schemes for finding the approximate minimizer of a constrained convex minimization problem and prove that the sequences generated by our schemes converge strongly to a solution of the constrained convex minimization problem such a solution is also a solution of a variational inequality defined over the set of fixed points of a nonexpansive mapping the results of this paper extend and improve several results presented in the literature in the recent past

an inequality of ostrowski gruss type and its applications to the estimation of error bounds for some special means and for some numerical quadrature rules abstract in this paper we derive a new inequality of ostrowski gruss type and apply it to the estimation of error bounds for some special means and for some numerical quadrature rules

strong convergence theorems for nonexpansive mappings and nonexpansive semigroups in this paper we show strong convergence theorems for nonexpansive mappings and nonexpansive semigroups in hilbert spaces by the hybrid method in the mathematical programming

strong convergence theorems of modified mann iterative process for strict pseudo contractions in hilbert spaces abstract in this paper we modify the normal mann s iterative process to have strong convergence for a k strictly pseudo contractive non self mapping in the framework of hilbert spaces our results improve and extend the corresponding results announced by many others

some new error inequalities for a generalized quadrature rule of open type some new error inequalities for a generalized quadrature rule of open type are established especially two sharp inequalities are derived when n is an odd and an even integer respectively

inference on the order of a normal mixture finite normal mixture models are used in a wide range of applications hypothesis testing on the order of the normal mixture is an important yet unsolved problem existing procedures often lack a rigorous theoretical foundation many are also hard to implement numerically in this article we develop a new method to fill the void in this important area an effective expectation maximization em test is invented for testing the null hypothesis of arbitrary order m 0 under a finite normal mixture model for any positive integer m 0 2 the limiting distribution of the proposed test statistic is we also use a novel computer experiment to provide empirical formulas for the tuning parameter selection the finite sample performance of the test is examined through simulation studies real data examples are provided the procedure has been implemented in r code the p values for testing the null order of m 0 2 or m 0 3 can be calculated with a single command this article has supplementary materials avail

error inequalities for a quadrature formula and applications an optimal two point quadrature formula of open type is derived it is shown that the optimal quadrature formula has a better error bound than the well known two point gaus quadrature formula various error inequalities for this formula are established applications in numerical integration are given

improvement and further generalization of inequalities of ostrowski gruss type abstract we improve some inequalities of ostrowski gruss type and further generalize them we apply the obtained results to the estimation of error bounds for some numerical quadrature rules also some bounds for the differences of some special means are discussed

a unified approach to some inequalities of ostrowski gruss type based on the euler maclaurin formula in the spirit of 1 we provide a unified approach to some inequalities of ostrowski gruss type which include some existing results as special cases some illustrative examples are also included

a new way to think about ostrowski like type inequalities in this present paper by considering some known inequalities of ostrowski like type we propose a new way to treat a class of ostrowski like type inequalities involving n points and m th derivative to be precise the following inequality email protected a bf x email protected i 1nf a x i b a 2m 54 b a m 1 m 1 s s holds where email protected sup a x bf m x email protected inf a x bf m x and for suitable x 1 x 2 x n it is worth noticing that n m are arbitrary numbers this means that the estimate in is more accurate when m is large enough our approach is also elementary

a general composite iterative algorithm for nonexpansive mappings in hilbert spaces let h be a real hilbert space suppose that t is a nonexpansive mapping on h with a fixed point f is a contraction on h with coefficient email protected 0 1 f h h is a k lipschitzian and h strongly monotone operator with k 0 h 0 and a h h is a strongly positive bounded linear operator with coefficient email protected email protected 1 2 let 0 0 where a n 0 1 and b n 0 1 converges strongly to a fixed point email protected email protected fix t which solves the variational inequality 0 email protected fix t

on the generalization of ostrowski and gruss type discrete inequalities abstract the main purpose of this paper is to establish a generalization of discrete inequalities of the ostrowski and gruss type involving two functions the analysis used in the proofs is fairly elementary

a unified generalization of some quadrature rules and error bounds by introducing a parameter we give a unified generalization of some quadrature rules which not only unify the recent results about error bounds for generalized mid point trapezoid and simpson s rules but also give some new error bounds for other quadrature rules as special cases especially two sharp error inequalities are derived when n is an odd and an even integer respectively

a sharp estimate for the peano error representation we provide a sharp estimate of the peano error representation formula for linear functionals as applications we obtain sharp estimates for the remainder term in general quadrature formulae and expand some ostrowski like type inequalities to linear functionals the new approach extends and unifies many earlier results on the subject dragomir and wang 1997 cheng 2001 matic 2003 vong 2011 gonska et al 2012