consistent tangent matrices for substepping schemes a very simple and general expression of the consistent tangent matrix for substepping time integration schemes is presented if needed the derivatives required for the computation of the consistent tangent moduli can be obtained via numerical differentiation these two strategies substepping and numerical differentiation lead to quadratic convergence in complex nonlinear inelasticity problems

hybrid iterative scheme for fixed point problem infinite systems of equilibrium and variational inequality problems the purpose of this paper is to construct a new iterative scheme by the hybrid method and prove a strong convergence theorem for the approximation of a common fixed point of two countable families of weak relatively nonexpansive mappings which is also a common solution to infinite systems of equilibrium and variational inequality problems in a uniformly smooth and strictly convex real banach space with kadec klee property using the properties of a generalized f projection operator using this result we give some applications our results extend many known recent results in the literature

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

effective properties of composite materials with periodic microstructure a computational approach abstract this study reviews several problems which are specific of composites with periodic microstructure composed of linear or nonlinear constituents the theoretical background of the method is recalled first two different families of numerical methods are considered to solve the problem the first is based on the finite element method the concept of macroscopic degrees of freedom is presented the implementation of periodicity conditions is discussed a general framework permitting either a strain or stress control is proposed the second numerical method is based on fast fourier transforms it considers first the problem of a homogeneous linear reference material undergoing a nonhomogeneous periodic eigenstrain the solution of this problem is based on the explicit form of the periodic green s function of the reference medium the relative merits of the two methods are compared and several examples are discussed both methods give very comparable results on test examples and their domains of applications appear to be complementary

strong convergence theorems for equilibrium problems and relatively nonexpansive mappings in banach spaces the purpose of the paper is to introduce modified halpern and ishikawa iteration for finding a common element of the set of fixed points of a relatively nonexpansive mapping and the set of solutions of an equilibrium problem in banach spaces we also consider two strong convergence theorems for relatively nonexpansive mappings with some proper restriction

convergence of the modified mann s iteration method for asymptotically strict pseudo contractions abstract let c be a closed convex subset of a real hilbert space h and assume that t is an asymptotically 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 modified mann s algorithm generates a sequence x n via the formula x n 1 n x n 1 n t n x n n 0 it is proved that if the control sequence n is chosen so that n 1 for some 0 1 then x n converges weakly to a fixed point of t we also modify this iteration method by applying projections onto suitably constructed closed convex sets to get an algorithm which generates a strongly convergent sequence

on some algorithms in banach spaces finding fixed points of nonlinear mappings abstract by using a modification of the hybrid method in mathematical programming we give some new algorithm to find out a fixed point of mappings which are in some sense non expansive our results hold in reflexive strictly convex smooth banach spaces with the kadec klee property

strong convergence theorems for monotone mappings and relatively weak nonexpansive mappings in this paper we prove strong convergence theorems to a zero of monotone mapping and a fixed point of relatively weak nonexpansive mapping moreover strong convergence theorems to a point which is a fixed point of relatively weak nonexpansive mapping and a solution of a certain variational problem are proved under appropriate conditions

approximating fixed points of nonexpansive mappings in a banach space by metric projections abstract in this paper a strong convergence theorem for nonexpansive mappings in a uniformly convex and smooth banach space is proved by using metric projections this theorem is different from the recent strong convergence theorem due to xu h k xu strong convergence of approximating fixed point sequences for nonexpansive mappings bull aust math soc 74 2006 143 151 which was established by generalized projections

universal anisotropic yield criterion based on superquadric functional representation part 1 algorithmic issues and accuracy analysis abstract a robust and efficient stress update algorithm for the anisotropic yield criterion represented in the form of superquadric function introduced by barlat et al is presented it relies on a discrete variational formulation of the lagrangian functional which results from the principle of maximum plastic dissipation numerical solution of the discretized equations of evolution is based on the operator split methodology and the newton raphson method a line search algorithm is implemented to overcome numerical instabilities and to expand the convergence region of the basic newton raphson solution procedure the consistent tangent modulus is expressed in a closed form as a result of the exact linearization of the discrete kuhn tucker condition numerical testing of the integration algorithm based on iso error maps is provided for several variants of the yield function

classical linear algebra inequalities for the jordan models of c0 operators abstract we extend to the class c 0 certain inequalities relating the sizes of the jordan blocks of a matrix with those of a restriction compression of the matrix the proofs seem to be more natural than those in the original linear algebra approach

an iterative algorithm for approximating solutions of hammerstein equations with monotone maps in banach spaces abstract let e l p 1 u k f u 0 has a solution u a coupled iterative process is constructed and proved to converge strongly to u furthermore our technique of proof is of independent interest

realization of the hybrid method for mann iterations abstract the mann iterations for nonexpansive mappings have only weak convergence even in a hilbert space h in order to overcome this weakness nakajo and takahashi proposed the hybrid method for mann s iteration process x 0 c chosen arbitrarily y n n x n 1 n tx n c n z c y n z x n z q n z c x 0 x n z x n 0 x n 1 p c n q n x 0 n 0 1 2 where c is a nonempty closed convex subset of h t c c is a nonexpansive mapping and p k is the metric projection from h onto a closed convex subset k of h however it is difficult to realize this iteration process in actual computing programs because the specific expression of p c n q n x 0 cannot be got in general in the case where c h we obtain the specific expression of p c n q n x 0 and thus the hybrid method for mann s iteration process can be realized easily numerical results show advantages of our result

hybrid approximation of solutions of nonlinear operator equations and application to equation of hammerstein type in this paper we study hybrid iterative scheme for finding a common element of set of solutions of generalized mixed equilibrium problem set of common fixed points of finite family of weak relatively nonexpansive mapping and null spaces of finite family of inverse strongly monotone mappings in a 2 uniformly convex and uniformly smooth real banach space our results extend improve and generalize the results of several authors which are announced recently application of our theorem to solution of equations of hammerstein type is of independent interest

monotone cq iteration processes for nonexpansive semigroups and maximal monotone operators abstract nakajo and takahashi k nakajo w takahashi strong convergence theorems for nonexpansive mappings and nonexpansive semigroups j math anal appl 279 2003 372 379 proved strong convergence theorems for nonexpansive mappings nonexpansive semigroups and the proximal point algorithm for zero point of monotone operators in hilbert spaces by the cq iteration method the purpose of this paper is to modify the cq iteration method of k nakajo and w takahashi using the monotone cq method and to prove strong convergence theorems in the proof process of this article the cauchy sequence method is used so we proceed without use of the demiclosedness principle and opial s condition and other weak topological techniques

a sub stepping scheme for multi scale analysis of solids abstract this paper proposes a sub stepping procedure aimed at saving overall computing time in the finite element solution of non linear solid mechanics problems where homogenization based multi scale constitutive models are used to describe the material response the procedure obtains better initial guesses for the newton raphson scheme adopted in the solution of the incremental equilibrium problem of the representative volume element rve associated with each gauss quadrature point of the discretised macroscopic continuum the resulting gain in robustness of the rve newton raphson iteration allows larger time load steps to be prescribed at the macroscopic scale leading to substantial savings in computing time the proposed sub stepping preserves the quadratic rate of asymptotic convergence of the macroscopic scale newton raphson scheme without compromising the accuracy of the solution numerical examples demonstrate that the achieved improvement in efficiency is particularly noticeable under the assumption of finite stains where overall speed up factors of up to four are observed

strong convergence of modified ishikawa iteration for two asymptotically nonexpansive mappings and semigroups abstract in this paper we established strong convergence theorems for a common fixed point of two asymptotically nonexpansive mappings and for a common fixed point of two asymptotically nonexpansive semigroups by using the hybrid method in a hilbert space moreover we also proved a strong convergence theorem for a common fixed point of two nonexpansive mappings our results extend and improve the recent ones announced by kim and xu t w kim h w xu strong convergence of modified mann iteration for asymptotically nonexpansive mappings and semigroups nonlinear anal 64 2006 1140 1152 nakajo and takahashi k nakajo w takahashi strong convergence theorems for nonexpansive mappings and nonexpansive semigroups j math anal appl 279 2003 372 379 and many others

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

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

strong convergence theorems for a finite family of asymptotically nonexpansive mappings and semigroups strong convergence theorems are obtained for a finite family of asymptotically nonexpansive mappings and semigroups by the modified mann method

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

nonlinear multi scale homogenization with different structural models at different scales summary we present an extension of the computational homogenization theory to cases where different structural models are used at different scales and no energy potential can be defined at the small scale we observe that volumetric averaging which is not applicable in such cases unless similarities exist in the macro scale and micro scale models is not a necessary prerequisite to carry out computational homogenization at each material point of the macro model we replace the conventional representative volume element with a representative domain element rde to link the large scale and small scale problems we then introduce a linear operator mapping the smooth part of the small scale displacement field of each rde to the large scale strain field and a trace operator to impose boundary conditions in the rde the latter is defined on the basis of engineering judgement analogously to the conventional theory a generalized hill s condition rather than being invoked is derived from duality principles and is used to recover the stress measures at the large scale for the implementation in a nonlinear finite element analysis control nodes and constraint equations are used the effectiveness of the procedure is demonstrated for three beam to truss example problems for which multi scale convergence is numerically analysed copyright 2013 john wiley sons ltd

strong convergence studied by a hybrid type method for monotone operators in a banach space abstract in this paper we study a strong convergence for monotone operators we first introduce the hybrid type algorithm for monotone operators next we obtain a strong convergence theorem theorem 3 3 for finding a zero point of an inverse strongly monotone operator in a banach space finally we apply our convergence theorem to the problem of finding a minimizer of a convex function

two scale kinematics and linearization for simultaneous two scale analysis of periodic heterogeneous solids at finite strain abstract we introduce the notion of two scale kinematics and the procedure of two scale linearization which are indispensable to the simultaneous two scale analysis method for the mechanical behavior of periodic heterogeneous solids at finite strain these are accomplished by formulating the two scale boundary value problem in both material and spatial descriptions with reference to the two scale modeling strategy developed in comput methods appl mech engrg 190 40 41 2001 5427 that utilized the convergence results of mathematical homogenization the formulation brings the intimate relationship between micro and macro scale kinematics in describing the micro macro coupling behavior inherent in heterogeneous media it is also shown that the two scale linearization necessitates the strict consistency with the micro scale equilibrated state and naturally invites the tangential homogenization process for both material and spatial descriptions several numerical examples of simultaneous two scale computations are presented to illustrate the two scale nature of the deformation of a heterogeneous solid at finite strain

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

homogenization based multiscale crack modelling from micro diffusive damage to macro cracks the existence of a representative volume element rve for a class of quasi brittle materials having a random heterogeneous microstructure in tensile shear and mixed mode loading is demonstrated by deriving traction separation relations which are objective with respect to rve size a computational homogenization based multiscale crack modelling framework implemented in an fe2 setting for quasi brittle solids with complex random microstructure is presented the objectivity of the macroscopic response to the micro sample size is shown by numerical simulations therefore a homogenization scheme which is objective with respect to macroscopic discretization and microscopic sample size is devised numerical examples including a comparison with direct numerical simulation are given to demonstrate the performance of the proposed method

convergence theorems of common fixed points for a family of lipschitz quasi pseudocontractions abstract in an infinite dimensional hilbert space the normal mann s iteration has only weak convergence in general even for nonexpansive mappings the purpose of this paper is to modify the normal mann s iteration to have strong convergence for a family of lipschitz quasi pseudocontractions in the framework of hilbert spaces our results improve and extend the corresponding ones announced by many others

quasiaffine orbits of invariant subspaces for uniform jordan operators abstract we consider the problem of classification of invariant subspaces for the class of uniform jordan operators we show that given two invariant subspaces m 1 and m 2 of a uniform jordan operator t s s the subspace m 2 belongs to the quasiaffine orbit of m 1 if and only if the restrictions t m 1 and t m 2 are quasisimilar and the compression t m 2 can be injected in the compression t m 1 our result refines previous work on the subject by bercovici and smotzer

computational micro to macro transitions for discretized micro structures of heterogeneous materials at finite strains based on the minimization of averaged incremental energy the paper investigates algorithms for the computation of homogenized stresses and overall tangent moduli of micro structures undergoing large strain deformations typically these micro structures define representative volumes of nonlinear heterogeneous materials such as inelastic composites polycrystalline aggregates or particle assemblies we consider a priori given discretized micro structures without focussing on details of specific discretization techniques for space and time the key contribution of the paper is the construction of a family of algorithms and matrix representations of overall properties of discretized micro structures which are motivated by a minimization of averaged incremental energy it is shown that the overall stresses and tangent moduli of a typical micro structure may exclusively be defined in terms of discrete forces and stiffness properties on the boundary we focus on deformation driven micro structures where the overall macroscopic deformation is controlled in this context three classical types of boundary conditions are investigated i linear deformation ii uniform tractions and iii periodic deformation and antiperiodic tractions incorporated by lagrangian multiplier methods these conditions generate three classes of constrained minimization problems with associated solution algorithms for the computation of equilibrium states and overall properties of micro structures the proposed algorithms and matrix representations of the overall properties are formally independent of the interior spatial structure and the local constitutive response of the micro structure and are therefore applicable to a broad class of model problems we demonstrate their performance for some representative model problems including finite elastic plastic deformations of composites texture developments in polycrystalline materials and equilibrium states of particle assemblies

the extragradient method for finding a common solution of a finite family of variational inequalities and a finite family of fixed point problems in the presence of computational errors abstract in a hilbert space we study the convergence of the subgradient method to a common solution of a finite family of variational inequalities and of a finite family of fixed point problems under the presence of computational errors most results known in the literature establish the convergence of algorithms when computational errors are summable in the present paper the convergence of the subgradient method is established for nonsummable computational errors we show that the subgradient method generates a good approximate solution if the sequence of computational errors is bounded from above by a constant

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

an algorithm for finding a common point of the solution set of a variational inequality and the fixed point set of a bregman relatively nonexpansive mapping in this paper we investigate an iterative scheme for finding a common point of the solution set of a variational inequality and the fixed point set of a bregman relatively nonexpansive mapping moreover a numerical example which shows the conclusion of our result is presented our results improve and generalize many known results in the current literature

t class algorithms for pseudocontractions and κ strict pseudocontractions in hilbert spaces in this paper we study iterative algorithms for finding a common element of the set of fixed points of strict pseudocontractions or finding a solution of a variational inequality problem for a monotone lipschitz continuous mapping the last problem being related to finding fixed points of pseudocontractions these algorithms were already studied in 1 and 9 but our aim here is to provide the links between these know algorithms and the general framework of t class algorithms studied in 3

convergence theorems for equilibrium problem variational inequality problem and countably infinite relatively quasi nonexpansive mappings in this paper we introduce an iterative process which converges strongly to a common element of set of common fixed points of countably infinite family of closed relatively quasi nonexpansive mappings the solution set of generalized equilibrium problem and the solution set of the variational inequality problem for a inverse strongly monotone mapping in banach spaces our theorems improve generalize unify and extend several results recently announced

quasisimilarity of invariant subspaces for uniform jordan operators of infinite multiplicity abstract let t be a bounded linear operator on a separable hilbert space h and let m and n be two invariant subspaces for t we will say that m and n are quasisimilar if there exist quasiaffinities i e bounded one to one operators with dense ranges x and y commuting with t such that x m n and y n m recall that operators t and t are quasisimilar if there exist quasiaffinities x h h and y h h such that xt t x and yt ty we show that if t is a uniform jordan operator of infinite multiplicity then m is quasisimilar to n if and only if t m is quasisimilar to t n and t m is quasisimilar to t n

a modified hybrid projection method for solving generalized mixed equilibrium problems and fixed point problems in banach spaces in this paper we introduce a modified new hybrid projection method for finding the set of solutions of the generalized mixed equilibrium problems and the convex feasibility problems for an infinite family of closed and uniformly quasi asymptotically nonexpansive mappings strong convergence theorems are established in a uniformly smooth and strictly convex banach space which also enjoys the kadec klee property our results improve and extend the corresponding results announced by qin et al 2010 and many authors

an adaptive sub incremental strategy for the solution of homogenization based multi scale problems abstract in this contribution several schemes for the solution of homogenization based multi scale constitutive problems undergoing finite strains with inelastic material behavior are investigated these schemes are aimed at improving the robustness and efficiency of the newton raphson method in the multilevel finite element ml fem framework an adaptive sub incremental strategy is proposed for the discrete representative volume element rve boundary value problem the procedure is able to ensure the convergence of the solution algorithm in the presence of several sources of non linearity and obtains improved initial guesses for the newton raphson scheme in the ml fem framework the enlargement of the convergence bowl of the newton raphson procedure at the micro scale allows larger macroscopic deformation gradients to be prescribed and significantly reduces the overall computational cost of ml fem analyses the proposed strategy preserves the quadratic rates of asymptotic convergence that characterize the newton raphson scheme at the macroscopic level numerical examples of both micro scale and two scale finite element simulations are presented to demonstrate the improved robustness and efficiency of the solution procedures proposed

convergence theorems for mixed equilibrium problems variational inequality problem and uniformly quasi ϕ asymptotically nonexpansive mappings abstract we introduce a modified block hybrid projection algorithm for finding a common element of the set of common fixed points of an infinite family of closed and uniformly quasi asymptotically nonexpansive mappings the set of the variational inequality for an inverse strongly monotone operator the set of solutions of the mixed equilibrium problems then we obtain strong convergence theorems for the sequences generated by this process in a 2 uniformly convex and uniformly smooth banach space our results extend and improve ones from several earlier works

an iterative method for equilibrium problems and a finite family of relatively nonexpansive mappings in a banach space abstract in this paper we introduce a new iterative method for finding a common element of the set of fixed points of a finite family of relatively nonexpansive mappings and the set of solutions of an equilibrium problem in uniformly convex and uniformly smooth banach spaces then we prove a strong convergence theorem by using the generalized projection

degree of convergence of modified averaged iterations for fixed points problems and operator equations abstract let h be a real hilbert space we propose a modification for averaged mappings to approximate the unique fixed point of a mapping t h h such that t is boundedly lipschitzian and t is monotone we not only prove strong convergence theorems but also determine the degree of convergence using this result an iteration process is given for finding the unique solution of the equation a x f where a h h is strongly monotone and boundedly lipschitzian

strong convergence of the cq method for fixed point iteration processes strong convergence theorems are obtained for the cq method for an ishikawa iteration process a contractive type iteration process for nonexpansive mappings and the proximal point algorithm for maximal monotone operators in hilbert spaces

a hybrid iteration scheme for equilibrium problems variational inequality problems and common fixed point problems in banach spaces abstract in this paper we introduce an iterative process which converges strongly to a common element of a set of common fixed points of finite family of closed relatively quasi nonexpansive mappings the solution set of generalized equilibrium problem and the solution set of the variational inequality problem for an inverse strongly monotone mapping in banach spaces

strong convergence theorems obtained by a generalized projections hybrid method for families of mappings in banach spaces abstract let c be a nonempty closed and convex subset of a uniformly convex and smooth banach space and let t n be a family of mappings of c into itself such that the set of all common fixed points of t n is nonempty we consider a sequence x n generated by the hybrid method by generalized projection in mathematical programming we give conditions on t n under which x n converges strongly to a common fixed point of t n and generalize the results given in 12 14 13 11

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 theorem of an iterative method for variational inequalities and fixed point problems in hilbert spaces in this paper we introduce a new iteration method based on the hybrid method in mathematical programming and the descent like method for finding a common element of the set of solutions for a variational inequality and the set of fixed points for a nonexpansive mapping in hilbert spaces our method modifies and improves some methods in literature

strong convergence theorems for a countable family of quasi lipschitzian mappings and its applications abstract we use the hybrid method in mathematical programming to obtain strong convergence to common fixed points of a countable family of quasi lipschitzian mappings as a consequence several convergence theorems for quasi nonexpansive mappings and asymptotically strict pseudo contractions are deduced we also establish strong convergence of iterative sequences for finding a common element of the set of fixed point the set of solutions of an equilibrium problem and the set of solutions of a variational inequality with an appropriate setting we obtain the corresponding results due to tada takahashi and nakajo shimoji takahashi

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

cyclic row contractions and rigidity of invariant subspaces abstract it is known that pure row contractions with one dimensional defect spaces can be classified up to unitary equivalence by compressions of the standard d shift acting on the full fock space upon settling for a softer relation than unitary equivalence we relax the defect condition and simply require the row contraction to admit a cyclic vector we show that cyclic pure row contractions can be transformed in a precise technical sense into compressions of the standard d shift cyclic decompositions of the underlying hilbert spaces are the natural tool to extend this fact to higher multiplicities we show that such decompositions face multivariate obstacles of an algebraic nature nevertheless decompositions are obtained for nilpotent commuting row contractions by analyzing function theoretic rigidity properties of their invariant subspaces

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

strong convergence theorems by halpern mann iterations for relatively nonexpansive mappings in banach spaces abstract in this paper we modify halpern and mann s iterations for finding a fixed point of a relatively nonexpansive mapping in a banach space consequently a strong convergence theorem for a nonspreading mapping is deduced using a concept of duality theorems we also obtain analogue results for certain generalized nonexpansive and generalized nonexpansive type mappings finally we discuss two strong convergence theorems concerning two types of resolvents of a maximal monotone operator in a banach space

strong convergence of a proximal type algorithm in a banach space in this paper we study strong convergence of the proximal point algorithm it is known that the proximal point algorithm converges weakly to a solution of a maximal monotone operator but it fails to converge strongly then in math program 87 2000 pp 189 202 solodov and svaiter introduced the new proximal type algorithm to generate a strongly convergent sequence and established a convergence property for it in hilbert spaces our purpose is to extend solodov and svaiter s result to more general banach spaces using this we consider the problem of finding a minimizer of a convex function

implicit iterative algorithms for asymptotically nonexpansive mappings in the intermediate sense and lipschitz continuous monotone mappings in this paper we introduce some implicit iterative algorithms for finding a common element of the set of fixed points of an asymptotically nonexpansive mapping in the intermediate sense and the set of solutions of the variational inequality problem for a monotone lipschitz continuous mapping these implicit iterative algorithms are based on two well known methods extragradient and approximate proximal methods we obtain some weak convergence theorems for these implicit iterative algorithms based on these theorems we also construct some implicit iterative processes for finding a common fixed point of two mappings such that one of these two mappings is taken from the more general class of lipschitz pseudocontractive mappings and the other mapping is asymptotically nonexpansive

iterative methods for strict pseudo contractions in hilbert spaces abstract let t i i 1 n be n strict pseudo contractions defined on a closed convex subset c of a real hilbert space h consider the problem of finding a common fixed point of these mappings and consider the parallel and cyclic algorithms for solving this problem we will prove the weak convergence of these algorithms moreover by applying additional projections we further prove that these algorithms can be modified to have strong convergence

strong convergence of modified mann iterations for asymptotically nonexpansive mappings and semigroups abstract the mann iterations for nonexpansive mappings have in general only weak convergence in a hilbert space we modify an iterative method of mann s type introduced by nakajo and takahashi strong convergence theorems for nonexpansive mappings and nonexpansive semigroups j math anal appl 279 2003 372 379 for nonexpansive mappings and prove strong convergence of our modified mann s iteration processes for asymptotically nonexpansive mappings and semigroups

numerical homogenization of periodic composite materials with non linear material components in this paper a numerically developed homogenized constitutive relation for the global behaviour of periodic composite materials with elasto plastic components is derived the algorithm presented is general and can be applied to any kind of non linear material behaviour respecting the complementarity rule the method different from those presented in the literature is currently restricted to small strains plane problems and monotonic proportional loading conditions copyright 1999 john wiley sons ltd

on a class of constitutive equations in viscoplasticity formulation and computational issues the viscoplastic constitutive model is formulated based on the existence of the dissipation potential which embodies the notion of the gauge minkowski function of the convex set a perturbation method is used for a solution of stiff differential equations characterizing the associated problem of evolution it relies on a discrete formulation of viscoplasticity which results from the regularized version of the principle of maximum plastic dissipation the operator split methodology and the newton raphson method are used to obtain the numerical solution of the discretized equations of evolution the consistent tangent modulus is expressed in a closed form as a result of the exact linearization of the discretized evolution equations for several variants of the flow potential function including some representative stiff functional forms numerical tests of the integration algorithm based on iso error maps are provided finally a numerical example is presented to illustrate the robustness and the effectiveness of the proposed approach

inequalities in banach spaces with applications well known that many problems in a hilbert space h are solved by applying the following identity ilax 1 a yi12 a412 1 llyl12 a 1 mx yl12 1 1 for all x y in h and 0 5 i 5 1 therefore one natural method to solve problems in a banach space xis to establish equalities and usually inequalities in xanalogous to 1 1 this is in fact shown by some authors recent work see for example reich l poffald and reich 2 lim 3 lim et af 4 prus and smarzewski 5 smarzewski 6 and reich 21 the purpose of this paper is to continue carrying out investigations in this line more precisely in section 3 we establish some inequalities analogous to 1 l in either uniformly convex or uniformly smooth banach spaces as corollaries we obtain new characteristics of p uniform convexity and q uniform smoothness of a banach space x via the functionals i lip and ii llq respectively we give in section 4 applications of the inequalities obtained in section 3 to fixed points of uniformly lipschitzian mappings and to best approximation theory

a hybrid scheme for finite families of equilibrium variational inequality and fixed point problems we introduce an iterative process for finding an element in the common fixed point set of finite family of closed relatively quasi nonexpansive mappings common solutions of finite family of equilibrium problems and common solutions of finite family of variational inequality problems for monotone mappings in banach spaces our theorem extends and unifies most of the results that have been proved for this important class of nonlinear operators

strong convergence theorem for pseudo contractive mappings in hilbert spaces abstract the purpose of this paper is to construct an ishikawa type of hybrid algorithm for pseudo contractive mappings in hilbert spaces our results extend the recent ones announced by yao et al y h yao y c liou g marino a hybrid algorithm for pseudo contractive mappings nonlinear anal 71 2009 4997 5002 and many others

asymptotically strict pseudocontractive mappings in the intermediate sense abstract it is proved that the modified mann iteration process x n 1 1 n x n n t n x n n n where n is a sequence in 0 1 with n 1 for some 0 1 converges weakly to a fixed point of an asymptotically strict pseudocontractive mapping t in the intermediate sense which is not necessarily lipschitzian we also develop cq method for this modified mann iteration process which generates a strongly convergent sequence