a fuzzy extension of the silhouette width criterion for cluster analysis the present paper proposes a new cluster validity measure as an additional criterion to help the decision making process in fuzzy cluster analysis this measure named fuzzy silhouette is a generalization to the fuzzy case of the average silhouette width criterion originally conceived to assess crisp non fuzzy data partitions the fuzzy silhouette is more appealing than its crisp counterpart in the context of fuzzy cluster analysis since it makes explicit use of the fuzzy partition matrix provided by the clustering algorithm in addition it has been designed to improve performance of the original silhouette criterion in detecting regions with higher data density when the data set involves overlapping clusters the performance of the fuzzy silhouette is evaluated and compared to that of five well known cluster validity measures six data sets are used to illustrate different scenarios in which the proposed fuzzy silhouette performs similar to or better than these other criteria thus becoming eligible to join a pool of measures to be used all together in fuzzy cluster analysis

autocorrelation based fuzzy clustering of time series the traditional approaches to clustering a set of time series are generally applicable if there is a fixed underlying structure to the time series so that each will belong to one cluster or the other however time series often display dynamic behaviour in their evolution over time this dynamic behaviour should be taken into account when attempting to cluster time series for instance during a certain period a time series might belong to a certain cluster afterwards its dynamics might be closer to that of another cluster in this case the traditional clustering approaches are unlikely to find and represent the underlying structure in the given time series this switch from one time state to another which is typically vague can be naturally treated following a fuzzy approach this paper proposes a fuzzy clustering approach based on the autocorrelation functions of time series in which each time series is not assigned exclusively to only one cluster but it is allowed to belong to different clusters with various membership degrees

on the convergence of hybrid projection algorithms for asymptotically quasi φ nonexpansive mappings using the mann iteration in an infinite dimensional hilbert space only weak convergence theorems are obtained even for nonexpansive mappings the purpose of this paper is to modify the mann iteration and prove the strong convergence theorems without any compactness assumption for asymptotically quasi f nonexpansive mappings moreover strong convergence theorems are also established in a uniformly smooth and strictly convex banach space with the kadec klee property

strong convergence theorems by hybrid methods for families of nonexpansive mappings in hilbert spaces abstract in this paper we prove a strong convergence theorem by the hybrid method for a family of nonexpansive mappings which generalizes nakajo and takahashi s theorems k nakajo w takahashi strong convergence theorems for nonexpansive mappings and nonexpansive semigroups j math anal appl 279 2003 372 379 simultaneously furthermore we obtain another strong convergence theorem for the family of nonexpansive mappings by a hybrid method which is different from nakajo and takahashi using this theorem we get some new results for a single nonexpansive mapping or a family of nonexpansive mappings in a hilbert space

shrinking projection methods for firmly nonexpansive mappings abstract the purpose of this paper is to study the shrinking projection method for firmly nonexpansive mappings the method gives us a strong convergence iteration for a family of firmly nonexpansive mappings and also permit us to obtain a sufficient condition for the existence of a fixed point of a firmly nonexpansive mapping

quantile autocovariances a powerful tool for hard and soft partitional clustering of time series abstract a key issue in cluster analysis is determining a proper dissimilarity measure between two data objects and many pairwise dissimilarities have been proposed to deal with time series assuming that the clustering purpose is to group series according to the underlying dependence structures a detailed study of the behavior in clustering of a dissimilarity based on comparing estimated quantile autocovariance functions qaf is carried out quantile autocovariances provide information about the serial dependence structure that other conventional features are not able to capture which suggests great potential to perform clustering of series the asymptotic behavior of the sample quantile autocovariances is studied and an algorithm to determine optimal combinations of lags and pairs of quantile levels to perform clustering is introduced the proposed metric is used to perform hard and soft partitioning based clustering first a broad simulation study examines the behavior of the proposed metric in crisp clustering with the pam procedure a novel fuzzy c medoids algorithm based on the qaf dissimilarity is then proposed and compared with other fuzzy procedures in a new simulation study conducted to cluster fuzzy scenarios involving ar and garch models in all cases the qaf based procedures outperform or are highly competitive with a range of dissimilarities reported in the literature particularly exhibiting high capability to cluster conditionally heteroskedastic time series and robustness to the distributional form of the errors two specific applications involving air quality data and financial time series illustrate the usefulness of the proposed procedures

on a hybrid method for a family of relatively nonexpansive mappings in a banach space we prove strong convergence theorems by the hybrid method given by takahashi takeuchi and kubota for a family of relatively nonexpansive mappings under weaker conditions the method of the proof is different from the original one and it shows that the type of projection used in the iterative method is independent of the properties of the mappings we also deal with the problem of finding a zero of a maximal monotone operator and obtain a strong convergence theorem using this method

approximations for nonlinear mappings by the hybrid method in hilbert spaces abstract the hybrid method in mathematical programming was introduced by haugazeau 1968 1 and he proved a strong convergence theorem for finding a common element of finite nonempty closed convex subsets of a real hilbert space later bauschke and combettes 2001 2 proposed some condition for a family of mappings the so called coherent condition and established interesting results by the hybrid method the authors nakajo et al 2009 10 extended bauschke and combettes s results in this paper we introduce a condition weaker than the coherent condition and prove strong convergence theorems which generalize the results of nakajo et al 2009 10 and we get strong convergence theorems for a family of asymptotically strict pseudo contractions a family of lipschitz and pseudo contractive mappings and a one parameter uniformly lipschitz semigroup of pseudo contractive mappings

a hybrid algorithm for pseudo contractive mappings abstract in this paper we suggest and analyze a hybrid algorithm for pseudo contractive mappings in hilbert spaces further we prove the strong convergence of the proposed iterative algorithm for lipschitz pseudo contractive mappings in hilbert spaces

convergence in norm of modified krasnoselski mann iterations for fixed points of demicontractive mappings abstract this paper deals with fixed points methods related to the general class of demicontractive mappings including the well known classes of nonexpansive and quasi nonexpansive mappings in hilbert spaces specifically we point out some historical aspects concerning the concept of demicontactivity and we investigate a regularized variant of the krasnoselski mann iteration that can be alternatively regarded as a simplified form of the inertial iteration p e mainge j math anal appl 344 2008 876 887 with non constant relaxation factors these two methods ensure the strong convergence of the generated sequence towards the least norm element of the set of fixed points of demicontractive mappings however for convergence our method does not require anymore the knowledge of some constant related to the involved demicontractive operator a new and simpler proof is also proposed for its convergence even when involving non constant relaxation factors we point out the simplicity of this algorithm at least from computational point of view in comparison with other existing methods we also present some numerical experiments concerning a convex feasibility problem experiments that emphasize the characteristics of the considered algorithm comparing with a classical cyclic projection type iteration

existence and iteration for a mixed equilibrium problem and a countable family of nonexpansive mappings in banach spaces we prove the existence of a solution of the mixed equilibrium problem mep by using the kkm mapping in a banach space setting then by virtue of this result we construct a hybrid algorithm for finding a common element in the solutions set of a mixed equilibrium problem and the fixed points set of a countable family of nonexpansive mappings in the frameworks of banach spaces by using a projection technique we also prove that the sequences generated by the hybrid algorithm converge strongly to a common element in the solutions set of mep and common fixed points set of nonexpansive mappings moreover some applications concerning the equilibrium and the convex minimization problems are obtained

convergence theorems for a countable family of lipschitzian mappings this paper is concerned with convergence of an approximating common fixed point sequence of countable lipschitzian mappings in a uniformly convex banach space we introduce a new condition for a class of mappings to obtain several weak and strong convergence theorems this new condition is implied by many previous known conditions introduced by many authors we also apply our results for a class of nonexpansive mappings and asymptotically nonexpansive mappings and we immediately obtain convergence theorems proved by song chen kimura takahashi tan xu and many others

two strong convergence theorems for bregman strongly nonexpansive operators in reflexive banach spaces abstract we study the convergence of two iterative algorithms for finding common fixed points of finitely many bregman strongly nonexpansive operators in reflexive banach spaces both algorithms take into account possible computational errors we establish two strong convergence theorems and then apply them to the solution of convex feasibility variational inequality and equilibrium problems

strong convergence to common fixed points of families of nonexpansive mappings abstract we introduce iteration schemes for families of nonexpansive mappings in hilbert spaces and prove that the iterates converge strongly to common fixed points of the mappings

a validity measure for fuzzy clustering the authors present a fuzzy validity criterion based on a validity function which identifies compact and separate fuzzy c partitions without assumptions as to the number of substructures inherent in the data this function depends on the data set geometric distance measure distance between cluster centroids and more importantly on the fuzzy partition generated by any fuzzy algorithm used the function is mathematically justified via its relationship to a well defined hard clustering validity function the separation index for which the condition of uniqueness has already been established the performance of this validity function compares favorably to that of several others the application of this validity function to color image segmentation in a computer color vision system for recognition of ic wafer defects which are otherwise impossible to detect using gray scale image processing is discussed

wavelets based clustering of multivariate time series crisp and fuzzy clustering methods based on a combination of univariate and multivariate wavelet features are considered for the clustering of multivariate time series the performance of each of these methods is evaluated for stationary and variance nonstationary multivariate time series with different error correlation structures the main outcomes of the simulation studies are are as follows the superior performance of this approach for both the crisp and fuzzy cluster methods compared to some of the other approaches for clustering multivariate time series the very good performance of the fuzzy relational method overall to cluster longer time series when all of them do not appear to group exclusively into well separated clusters we consider an application to multivariate greenhouse gases time series and show that the crisp and fuzzy clustering methods considered are well validated

finite covers of 3 manifolds containing essential tori it is shown in this paper that if a haken 3 manifold contains an incompressible torus that is not boundary parallel then either it has a finite cover that is a torus bundle over the circle or it has finite covers with arbitrarily large first betti number in he 4 hempel conjectures that every haken 3 manifold has a finite cover whose fundamental group has a nontrivial representation to the integers i e the group is indicable the conjecture is proved in this paper in the case that the haken manifold contains an incompressible torus in particular it is shown theorem 1 1 that if haken manifold contains an incompressible torus that is not boundaryparallel then either it has a finite cover that is a torus bundle over the circle or it has finite covers with arbitrarily large first betti number hempel s conjecture arises in the context of the following question 1 does every irreducible 3 manifold with infinite fundamental group have a finite cover which is haken an affirmative answer to this would be a big step toward the classification of 3 manifolds with infinite fundamental group how would one detect such a cover a common way of showing that an irreducible 3 manifold is haken is to show that its fundamental group has a nontrivial representation to the integers then use this fact to find a map from the 3 manifold to the circle for which the pre image of some regular value is an incompressible surface thus question 1 leads to 2 does every irreducible 3 manifold have a finite cover whose fundamental group has a nontrivial representation to the integers an affirmative answer to 2 would certainly imply one for 1 however the converse is not known in fact the conjecture of hempel stated in the first paragraph says exactly that 1 implies 2 for example let m be the union of two knot complements identified along their boundaries in such a way that the meridian of each knot complement is identified with the longitude of the other then m is haken but 7ti m has no nontrivial representation to the integers hy m 0 however it is shown in he 4 that in many cases m will have a finite cover whose fundamental group does have such a representation note that there m contains an incompressible torus that is not boundary parallel hence theorem 1 1 applies in fact the argument used to prove theorem 1 1 is a generalization of that used in he 4 for this example this paper is taken from part of the author s ph d dissertation and as such owes much to cameron gordon received by the editors february 20 1986 and in revised form september 16 1987 1980 mathematics subject classification 1985 revision primary 57m05 57m10 secondary 20e07 this work was supported in part by nsf grant dms 8504683 1988 american mathematical society 0002 9947 88 1 00 25 per page 381 license or copyright restrictions may apply to redistribution see http www ams org journal terms of use

group presentation p adic analytic groups and lattices in mathrm sl _2 mathbf c groups by using their pro p completions this method is based on the observation that if x r is a presentation of the finitely generated f g group f then x r considered as a presentation for a pro p group is actually a presentation for t the pro p completion of f first we prove a generalization of a theorem of golod and shafarevich cf h theorem let g be a p adic analytic pro p group different from zp the p adic integers if x r is a minimal presentation of g then 1x 2 iri 2

strong convergence theorems for solving equilibrium problems and fixed point problems of ξ strict pseudo contraction mappings by two hybrid projection methods in this paper we introduce an iterative scheme by using the hybrid projection methods for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a x strict pseudo contraction mapping in hilbert spaces we obtain two strong convergence theorems under mild assumptions on parameters for the sequences generated by these processes the results presented in the paper extend and improve some 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 336 346 tada and takahashi a tada w takahashi weak and strong convergence theorems for a nonexpansive mapping and an equilibrium problem j optim theory appl 133 2007 359 370 and ceng et al l c ceng s al homidan q h ansari j c yao an iterative scheme for equilibrium problems and fixed point problems of strict pseudo contraction mappings j comput appl math 223 2009 967 974 and many others

the quantilogram with an application to evaluating directional predictability abstract we propose a new diagnostic tool for time series called the quantilogram the tool can be used formally and we provide the inference tools to do this under general conditions and it can also be used as a simple graphical device we apply our method to measure directional predictability and to test the hypothesis that a given time series has no directional predictability the test is based on comparing the correlogram of quantile hits to a pointwise confidence interval or on comparing the cumulated squared autocorrelations with the corresponding critical value we provide the distribution theory needed to conduct inference propose some model free upper bound critical values and apply our methods to s p500 stock index return data the empirical results suggest some directional predictability in returns the evidence is strongest in mid range quantiles like 5 10 and for daily data the evidence for predictability at the median is of comparable strength to the evidence around the mean and is strongest at the daily frequency

on hybrid projection methods for asymptotically quasi φ nonexpansive mappings the purpose of this paper is to consider the problem of approximating a common fixed point of two asymptotically quasi f nonexpansive mappings based on hybrid projection methods strong convergence theorems are established in a real banach space

a hybrid algorithm with variable coefficients for asymptotically pseudocontractive mappings in the intermediate sense on unbounded domains abstract the purpose of this article is to propose a new hybrid algorithm with variable coefficients and prove convergence theorems for asymptotically pseudocontractive mappings in the intermediate sense on unbounded domains the results of the paper improve and extend the recent results of qin et al x l qin s y cho j k kim convergence theorems on asymptotically pseudocontractive mappings in the intermediate sense fixed point theory appl 2010 doi 10 1155 2010 186874 article id 186874 14 pages and several others the algorithm with variable coefficients introduced in this paper is of independent interest

generalized spectral tests for serial dependence summary two tests for serial dependence are proposed using a generalized spectral theory in combination with the empirical distribution function the tests are generalizations of the cramer von mises and kolmogorov smirnov tests based on the standardized spectral distribution function they do not involve the choice of a lag order and they are consistent against all types of pairwise serial dependence including those with zero autocorrelation they also require no moment condition and are distribution free under serial independence a simulation study compares the finite sample performances of the new tests and some closely related tests the asymptotic distribution theory works well in finite samples the generalized cramer von mises test has good power against a variety of dependent alternatives and dominates the generalized kolmogorov smirnov test a local power analysis explains some important stylized facts on the power of the tests based on the empirical distribution function

modified block iterative algorithm for quasi ϕ asymptotically nonexpansive mappings and equilibrium problem in banach spaces abstract the purpose of this paper is to propose a modified block iterative algorithm for find a common element of the set of common fixed points of an infinite family of quasi asymptotically nonexpansive mappings and the set of an equilibrium problem under suitable conditions some strong convergence theorems are established in a uniformly smooth and strictly convex banach space with the kadec klee property as an application at the end of the paper a numerical example is given the results presented in the paper improve and extend the corresponding results in qin et al convergence theorems of common elements for equilibrium problems and fixed point problem in banach spaces j comput appl math 225 2009 20 30 zhou et al convergence theorems of a modified hybrid algorithm for a family of quasi asymptotically nonexpansive mappings j appl math compt 17 march 2009 doi 10 1007 s12190 009 0263 4 takahashi and zembayshi strong and weak convergence theorems for equilibrium problems and relatively nonexpansive mappings in banach spaces nonlinear anal 70 2009 45 57 wattanawitoon and kumam strong convergence theorems by a new hybrid projection algorithm for fixed point problem and equilibrium problems of two relatively quasi nonexpansive mappings nonlinear anal hybrid syst 3 2009 11 20 and matsushita and takahashi a strong convergence theorem for relatively nonexpansive mappings in banach spaces j approx theory 134 2005 257 266 and others

strong convergence theorem for nonexpansive semigroups in hilbert space abstract the purpose of this paper is to prove the strong convergence of a method combining the descent method and the hybrid method in mathematical programming for finding a point in the common fixed point set of a semigroup of nonexpansive mappings in hilbert space

limit theory for the sample autocorrelations and extremes of a garch 1 1 process the asymptotic theory for the sample autocorrelations and extremes of a garch i 1 process is provided special attention is given to the case when the sum of the arch and garch parameters is close to 1 that is when one is close to an infinite variance marginal distribution this situation has been observed for various financial log return series and led to the introduction of the igarch model in such a situation the sample autocorrelations are unreliable estimators of their deterministic counterparts for the time series and its absolute values and the sample autocorrelations of the squared time series have nondegenerate limit distributions we discuss the consequences for a foreign exchange rate series

3 manifolds which admit finite group actions we prove several results which support the following conjectures 1 any smooth action of a finite group on a geometric 3 manifold can be conjugated to preserve the geometric structure 2 every irreducible closed 3 manifold m with infinite 1 m is finitely covered by a haken 3 manifold

the cross quantilogram measuring quantile dependence and testing directional predictability between time series this paper proposes the cross quantilogram to measure the quantile dependence between two time series we apply it to test the hypothesis that one time series has no directional predictability to another time series we establish the asymptotic distribution of the cross quantilogram and the corresponding test statistic the limiting distributions depend on nuisance parameters to construct consistent confidence intervals we employ the stationary bootstrap procedure we show the consistency of this bootstrap also we consider the self normalized approach which is shown to be asymptotically pivotal under the null hypothesis of no predictability we provide simulation studies and two empirical applications first we use the cross quantilogram to detect predictability from stock variance to excess stock return compared to existing tools used in the literature of stock return predictability our method provides a more complete relationship between a predictor and stock return second we investigate the systemic risk of individual financial institutions such as jp morgan chase goldman sachs and aig this article has supplementary materials online

viscosity approximations by the shrinking projection method in hilbert spaces we consider viscosity approximations by using the shrinking projection method established by takahashi takeuchi and kubota and the modified shrinking projection method proposed by qin cho kang and zhou for finding a common fixed point of countably many nonlinear mappings and we prove strong convergence theorems which extend some known results we also consider semigroups of nonlinear mappings and obtain strong convergence of iterative schemes which approximate a common fixed point of the semigroup under certain conditions

iterative methods for the computation of fixed points of demicontractive mappings this paper surveys some of the main convergence properties of the mann type iteration for the demicontractive mappings some variants of the mann iteration that ensure the strong convergence like the cq algorithm and a variant for the asymptotically demicontractive mappings are also considered the usual framework of our study is a real hilbert space and only to a certain extent some particular banach spaces historical aspects are pointed out and some applications for the convex feasibility problem are discussed

partitional fuzzy clustering methods based on adaptive quadratic distances this paper presents partitional fuzzy clustering methods based on adaptive quadratic distances the methods presented furnish a fuzzy partition and a prototype for each cluster by optimizing an adequacy criterion based on adaptive quadratic distances these distances change at each algorithm iteration and can either be the same for all clusters or different from one cluster to another moreover various fuzzy partition and cluster interpretation tools are introduced experiments with real and synthetic data sets show the usefulness of these adaptive fuzzy clustering methods and the merit of the fuzzy partition and cluster interpretation tools

orientation reversing involutions and the first betti number for finite coverings of 3 manifolds letm s 3 p 3 be a closed orientable irreducible 3 manifold which admits an orientation reversing involution m m if dim fix 0 suppose 1 m has a subgroup of even index we show thatm has finite coverm mm with 1 m 0 as an application we show that the hyperbolic dodecahedral space has a finite cover with positive 1st betti number

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

new monotone hybrid algorithm for hemi relatively nonexpansive mappings and maximal monotone operators the purpose of this article is to prove the strong convergence theorems for hemi relatively nonexpansive mappings in banach spaces in order to get the strong convergence theorems for hemi relatively nonexpansive mappings a new monotone hybrid iteration algorithm is presented and is used to approximate the fixed point of hemi relatively nonexpansive mappings noting that the general hybrid iteration algorithm can be used for relatively nonexpansive mappings but it can not be used for hemi relatively nonexpansive mappings however this new monotone hybrid algorithm can be used for hemi relatively nonexpansive mappings in addition a new method of proof has been used in this article that is by using this new monotone hybrid algorithm we firstly claim that the iterative sequence is a cauchy sequence the results of this paper modify and improve the results of matsushita and takahashi and some others

strong convergence of shrinking projection methods for quasi φ nonexpansive mappings and equilibrium problems the purpose of this paper is to consider the convergence of a shrinking projection method for a finite family of quasi f nonexpansive mappings and an equilibrium problem strong convergence theorems are established in a uniformly smooth and strictly convex banach space which also enjoys the kadec klee property

strong convergence theorems for an infinite family of quasi nonexpansive mappings and generalized equilibrium problems and variational inequality problems in this paper we introduce a new iterative scheme for finding a common element of the set of common fixed points of an infinite family of uniformly continuous quasi nonexpansive mappings and the set of solutions to a generalized equilibrium problem and the set of solutions to a variational inequality problem in a real hilbert space we then prove strong convergence of the scheme to a common element of the three mentioned sets our results extend important recent results

strong convergence for a countable family of strict pseudocontractions in q uniformly smooth banach spaces we introduce a new iterative algorithm for finding a common fixed point of a countable family of strict pseudocontractions in q uniformly smooth and uniformly convex banach spaces we then prove that the sequence generated by the proposed algorithm converges strongly to a common fixed point of an infinite family of strict pseudocontractions our results mainly improve and extend the results announced by yao et al y yao y c liou g marino strong convergence of two iterative algorithms for nonexpansive mappings in hilbert spaces fixed point theory appl 2009 2009 7 pages doi 10 1155 2009 279058 art id 279058

a hybrid iterative scheme for equilibrium problems and fixed point problems of asymptotically k strict pseudo contractions in this paper we propose an iterative scheme for finding a common element of the set of solutions of an equilibrium problem and the set of common fixed points of a finite family of asymptotically k strict pseudo contractions in the setting of real hilbert spaces by using our proposed scheme we get a weak convergence theorem for a finite family of asymptotically k strict pseudo contractions and then we modify these algorithm to have strong convergence theorem by using the two hybrid methods in the mathematical programming our results improve and extend the recent ones announced by ceng et al s result l c ceng al homidan q h ansari and j c yao an iterative scheme for equilibrium problems and fixed point problems of strict pseudo contraction mappings j comput appl math 223 2009 967 974 qin cho kang and shang x qin y j cho s m kang and m shang a hybrid iterative scheme for asymptotically k strict pseudo contractions in hilbert spaces nonlinear anal 70 2009 1902 1911 and other authors

strong convergence theorems for 2 generalized hybrid mappings in hilbert spaces abstract in this paper we prove a strong convergence theorem of halpern s type for 2 generalized hybrid mappings in a hilbert space we also deal with strong convergence theorems by hybrid methods for these nonlinear mappings in a hilbert space

approximation of common fixed points for a countable family of relatively nonexpansive mappings in a banach space and applications abstract in this paper we prove a strong convergence theorem by the hybrid method for a countable family of relatively nonexpansive mappings in a banach space we also establish a new control condition for the sequence of mappings t n which is weaker than the control condition in lemma 3 1 of aoyama et al k aoyama y kimura w takahashi and m toyoda approximation of common fixed points of a countable family of nonexpansive mappings in a banach space nonlinear anal 67 2007 2350 2360 moreover we apply our results for finding a common fixed point of two relatively nonexpansive mappings in a banach space and an element of the set of solutions of an equilibrium problem in a banach space respectively our results are applicable to a wide class of mappings

viscosity approximation methods for countable families of nonexpansive mappings in banach spaces abstract let c be a nonempty closed convex subset of a banach space e and let s n be a family of nonexpansive mappings of c into itself such that the set of common fixed points of s n is nonempty we first introduce a sequence x n of c defined by x 1 x c and x n 1 n f x n 1 n s n x n for all n n where n 0 1 and f is a contraction of c into itself further we give the conditions of n and s n under which x n converges strongly to a common fixed point of s n this result generalizes the strong convergence theorem for nonexpansive mappings by suzuki t suzuki a sufficient and necessary condition for halpern type strong convergence to fixed points of nonexpansive mappings proc amer math soc 135 2007 99 106 and the strong convergence theorem for accretive operators by kamimura and takahashi s kamimura w takahashi weak and strong convergence of solutions to accretive operator inclusions and applications set valued anal 8 2000 361 374 simultaneously using this result we improve and extend the two above mentioned results

a nonparametric test of serial independence based on the empirical distribution function the blum kiefer rosenblatt 1961 statistic for testing independence is considered in a time series setting this test is under mild conditions shown to be consistent against lag one dependent alternatives the null distribution of the test statistic is established both when the marginal distribution is continuous and when it is discrete simulation results giving information on the size and the power of the test are provided and comparisons are made with other tests of serial dependence an extension of the test is made to detect higher lag dependence and finally the test is applied to a real data example

strong convergence theorem by a new hybrid method for equilibrium problems and variational inequality problems abstract in this paper we prove a strong convergence theorem for finding a common element of the set of solutions of an equilibrium problem and the set of the solutions of the variational inequality problem by using a new hybrid method we obtain a new result for finding a solution of an equilibrium problem and the solutions of the variational inequality problem

projection algorithms for solving nonmonotone equilibrium problems in hilbert space we propose two projection algorithms for solving an equilibrium problem where the bifunction is not required to be satisfied any monotone property under assumptions on the continuity convexity of the bifunction and the nonemptyness of the solution set of the minty equilibrium problem we show that the sequences generated by the proposed algorithms converge weakly and strongly to a solution of the primal equilibrium problem respectively

modified hybrid algorithms for lipschitz quasi pseudo contractive mappings in hilbert spaces in this paper strong convergence theorems are obtained by modified hybrid methods for lipschitz quasi pseudo contractions in a hilbert space besides applications of these theorems are introduced finally we use these methods to modify ishikawa s iteration process and get some strong convergence theorems which are different from zhou h y zhou convergence theorems of fixed points for lipschitz pseudo contractions in hilbert spaces j math anal appl 343 2008 546 556