existence of nonexpansive retractions for amenable semigroups of nonexpansive mappings and nonlinear ergodic theorems in banach spaces in this paper we study nonlinear ergodic properties for an amenable semigroup of nonexpansive mappings in a banach space we prove that ifsis an amenable semigroup and s tt t s is a nonexpansive semigroup on a closed convex subsetcin a uniformly convex banach spaceesuch that the setf s of common fixed points of s is nonempty then there exists a nonexpansive retractionpfromcontof s such thatptt ttp pfor eacht sandpx co ttx t s for eachx c in this case there exists a net a of finite averages of s such that for eacht sand for each bounded subsetbofc lim a ttx a x 0 and lim tta x a x 0 uniformly forx b also if the norm ofeis frechet differentiable then for eachx c pxis the unique common fixed point in s s co ttsx t s furthermore if is an asymptotically invariant net of means then for eachx c t x converges weakly topx

a new mapping for finding common solutions of equilibrium problems and fixed point problems of finite family of nonexpansive mappings abstract in this paper we introduce and study a new mapping generated by a finite family of nonexpansive mappings and finite real numbers and introduce a general iterative method concerning the new mappings for finding a common element of the set of solutions of an equilibrium problem and of the set of common fixed points of a finite family of nonexpansive mappings in a hilbert space then we prove a strong convergence theorem of the proposed iterative method for a finite family of nonexpansive mappings to the unique solution of variational inequality which is the optimality condition for a minimization problem our main result can be applied to obtain strong convergence of the general iterative methods which are modifications of those in g marino h k xu a general iterative method for nonexpansive mappings in hilbert spaces j math anal appl 318 1 2006 43 52 s plubtieng r punpaeng a general iterative method for equilibrium problems and fixed point problems in hilbert spaces j math anal appl 336 1 2007 455 469 s takahashi w takahashi viscosity approximation methods for equilibrium problems and fixed point problems in hilbert spaces j math anal appl 331 1 2007 506 515 to a common element of the set of solutions of an equilibrium problem and the set of fixed points of a nonexpansive mapping

an iterative algorithm for solving fixed point problems variational inequality problems and mixed equilibrium problems abstract in this paper we introduce an iterative algorithm for finding a common element of the set of solutions of a mixed equilibrium problem the set of fixed points of an infinite family of nonexpansive mappings and the set of solutions of some variational inequality furthermore we prove that the proposed iterative algorithm converges strongly to a common element of the above three sets our results extend and improve the corresponding results of zeng and yao l c zeng and j c yao a hybrid iterative scheme for mixed equilibrium problems and fixed point problems j comput appl math 214 2008 186 201 takahashi and takahashi s takahashi and w takahashi viscosity approximation methods for equilibrium problems and fixed point problems in hilbert spaces j math anal appl 331 2007 506 515 and many others

some finitely presented nilpotent by abelian groups this paper gives some sufficient conditions for the finite presentability of nilpotent by abelian groups the general question of deciding whether a particular soluble group admits a finite presentation has received considerable attention in recent years see the review article of strebel lo for a discussion of the work to 1984 in particular we want to draw attention to three papers particularly relevant to the topic of this paper firstly bieri and strebel have given in 4 a necessary and sufficient condition for the finite presentation of a metabelian group the present work is based on their methods the sufficient condition was extended by mcisaac in 7 to a condition for the finite presentation of a split extension of a group of nilpotency class 2 by an abelian group in a major work abels 2 deals with finite presentability of arithmetic groups his work shows for example that soluble arithmetic groups corresponding to connected algebraic groups are finitely presented if and only if the metabelian quotient is finitely presented and the multiplier the second homology with trivial coefficients of the derived group is finitely generated as a module for the group this therefore gives a superb answer to the question for arithmetic groups but it is not clear to what extent such results are available for general abstract groups we return briefly to this later in this introduction the aim of this paper is to carry the sufficient condition given by mcisaac considerably further we remove the restriction that the extension involved be split and widen the condition considerably in particular we make use of the jacobi identity which did not figure in mcisaac s treatment we also extend the results to the case where the nilpotent normal subgroup has arbitrary nilpotency class to describe our results we need to introduce some notation and to

on projection algorithms for solving convex feasibility problems due to their extraordinary utility and broad applicability in many areas of classical mathematics and modern physical sciences most notably computerized tomography algorithms for solving convex feasibility problems continue to receive great attention to unify generalize and review some of these algorithms a very broad and flexible framework is investigated several crucial new concepts which allow a systematic discussion of questions on behaviour in general hilbert spaces and on the quality of convergence are brought out numerous examples are given

a general iterative method for equilibrium problems and fixed point problems 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 an equilibrium problem and the set of fixed points of a nonexpansive mapping in a hilbert space then we prove two strong convergence theorems for nonexpansive mappings to solve a unique solution of the variational inequality which is the optimality condition for the minimization problem these results extended and improved the corresponding results of marino and xu g marino h k xu a general iterative method for nonexpansive mapping in hilbert spaces j math anal appl 318 2006 43 52 s takahashi and w takahashi s takahashi w takahashi viscosity approximation methods for equilibrium problems and fixed point problems in hilbert spaces j math anal appl 331 1 2007 506 515 and many others

algorithms for approximating minimization problems in hilbert spaces in this paper we study the following minimization problem minx fix s w m2 12 x 2 h x where b is a bounded linear operator m 0 is some constant h is a potential function for c f fix t is the set of fixed points of nonexpansive mapping s and w is the solution set of an equilibrium problem this paper introduces two new algorithms one implicit and one explicit that can be used to find the solution of the above minimization problem

on iterative methods for equilibrium problems abstract in this paper we introduce a hybrid iterative scheme for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of finitely many nonexpansive mappings we prove that the approximate solution converges strongly to a solution of a class of variational inequalities under some mild conditions which is the optimality condition for some minimization problem we also give some comments on the results of plubtieng and punpaeng s plubtieng r punpaeng a general iterative method for equilibrium problems and fixed point problems in hilbert spaces j math anal appl 336 2007 455 469 results obtained in this paper may be viewed as an improvement and refinement of the previously known results in this area

correction global well posedness for the kp i equation as kindly pointed out by a faminskii the anisotropic sobolev inequality 7 inproposition 3 of 5 is not known to hold note that 7 is only used in the proofof propositions 7 8 in 5 propositions 7 8 of 5 however still hold as will beexplained here the main new point is the following extension of proposition 6of 5

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

the cauchy problem for the rotation modified kadomtsev petviashvili type equation abstract this paper is devoted to studying the cauchy problem for the rotation modified kadomtsev petviashvili rmkp type equation x u t x 3 u x u 2 y 2 u u 0 in the anisotropic sobolev spaces h s 1 s 2 r 2 when 0 and 0 0 we show that the cauchy problem is locally well posed in h s 1 s 2 r 2 with s 1 1 2 and s 2 0 the main difficulty in establishing bilinear estimates related to nonlinear term of rmkp type equation is that the resonant function 3 1 2 1 2 1 2 2 2 1 2 1 2 1 1 2 2 2 may tend to zero since 0 0 and 0 when 0 and 0 and 0 we also prove that the cauchy problem for rmkp equation is ill posed in h s 1 0 r 2 with s 1 1 2 in the sense that the flow map associated to the rotation modified kadomtsev petviashvili is not c 3

strong convergence theorems for finitely many nonexpansive mappings and applications abstract let e be a uniformly convex banach space which satisfies opial s condition or whose norm is frechet differentiable recently takahashi and shimoji w takahashi k shimoji convergence theorems for nonexpansive mappings and feasibility problems math comput modelling 32 2000 1463 1471 introduced an iterative scheme given by finitely many nonexpansive mappings in e and proved weak convergence theorems which are connected with the problem of image recovery in this paper we introduce a new iterative scheme which includes their iterative scheme as a special case under the assumption that e is a reflexive banach space whose norm is uniformly g teaux differentiable and which has a weakly continuous duality mapping we prove strong convergence theorems which are connected with the problem of image recovery using the established results we consider the problem of finding a common fixed point of finitely many nonexpansive mappings

existence of ergodic retractions for semigroups in banach spaces abstract in this work we prove among other results that if s is a right amenable semigroup and t s s s is a quasi nonexpansive semigroup on a closed convex subset c in a strictly convex reflexive banach space e such that the set f of common fixed points of is nonempty then there exists a quasi nonexpansive retraction p from c onto f such that p t t t t p p for each t s and every closed convex invariant subset of c is also p invariant moreover if the mappings are also affine then t g rode an ergodic theorem for semigroups of nonexpansive mappings in a hilbert space j math anal appl 85 1982 172 178 12 is a quasi contractive affine retraction from c onto f such that t t t t t t t for each t s and t x c o t t x t s for each x c and if r is an arbitrary retraction from c onto f such that r x c o t t x t s for each x c then r t it is shown that if the t t s are f quasi contractive then the results hold without the strict convexity condition on e

a new general iterative scheme for split variational inclusion and fixed point problems of k strict pseudo contraction mappings with convergence analysis in this paper we modify the general iterative method to approximate a common element of the set of solutions of split variational inclusion problem and the set of common fixed points of a finite family of k strictly pseudo contractive nonself mappings strong convergence theorem is established under some suitable conditions in a real hilbert space which also solves some variational inequality problems results presented in this paper may be viewed as a refinement and important generalizations of the previously known results announced by many other authors finally some examples to study the rate of convergence and some illustrative numerical examples are presented

strong convergence of krasnoselskii and mann s type sequences for one parameter nonexpansive semigroups without bochner integrals abstract in this paper we prove krasnoselskii and mann s type convergence theorems for nonexpansive semigroups without using bochner integral and without assuming the strict convexity of banach spaces one of our main results is the following let c be a compact convex subset of a banach space e and let t t t 0 be a one parameter strongly continuous semigroup of nonexpansive mappings on c let t n be a sequence in 0 satisfying lim inf n t n lim sup n t n and lim n t n 1 t n 0 let 0 1 define a sequence x n in c by x 1 c and x n 1 t t n x n 1 x n for n n then x n converges strongly to a common fixed point of t t t 0

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

viscosity approximation methods for nonexpansive mappings abstract viscosity approximation methods for nonexpansive mappings are studied consider a nonexpansive self mapping t of a closed convex subset c of a banach space x suppose that the set fix t of fixed points of t is nonempty for a contraction f on c and t 0 1 let x t c be the unique fixed point of the contraction x tf x 1 t tx consider also the iteration process x n where x 0 c is arbitrary and x n 1 n f x n 1 n tx n for n 1 where n 0 1 if x is either hilbert or uniformly smooth then it is shown that x t and under certain appropriate conditions on n x n converge strongly to a fixed point of t which solves some variational inequality

global well posedness of the kp i initial value problem in the energy space we prove that the kp i initial value problem begin cases partial tu partial x 3u partial x 1 partial y 2u partial x u 2 2 0 text on mathbb r 2 x y times mathbb r t u 0 phi end cases is globally well posed in the energy space mathbf e 1 mathbb r 2 big phi mathbb r 2 to mathbb r phi mathbf e 1 mathbb r 2 approx phi l 2 partial x phi l 2 big partial x 1 partial y phi big l 2 infty big

a system of mixed equilibrium problems fixed point problems of strictly pseudo contractive mappings and nonexpansive semi groups the purpose of this paper is to introduce an iterative algorithm for finding a common element of the set of solutions for a system of mixed equilibrium problems the set of common fixed points for an infinite family of strictly pseudo contractive mappings and the set of common fixed points for nonexpansive semi groups in hilbert space under suitable conditions some strong convergence theorem are proved the results presented in the paper extend and improve some recent results

a new algorithm for two finite families of demicontractive mappings and equilibrium problems in this paper we introduce a new algorithm for finding a common element of the set of solutions of an equilibrium problem and the set of common fixed points of two finite families of demicontractive mappings the strong convergence theorem of the proposed algorithm is established under some suitable control conditions in a real hilbert space our result generalizes several recent results in the current literature

an iterative method for finding common solutions of equilibrium and fixed point problems we introduce an iterative method for finding a common element of the set of solutions of an equilibrium problem and of the set of fixed points of a finite family of nonexpansive mappings in a hilbert space we prove the strong convergence of the proposed iterative algorithm to the unique solution of a variational inequality which is the optimality condition for a minimization problem

iterative algorithms for finding common solutions of variational inequalities and systems of equilibrium problems and fixed points of families and semigroups of nonexpansive mappings abstract we introduce iterative algorithms for finding a common element of the set of solutions of a system of equilibrium problems and of the set of fixed points of a finite family and a left amenable semigroup of nonexpansive mappings in a hilbert space we prove the strong convergence of the proposed iterative algorithm to the unique solution of a variational inequality which is the optimality condition for a minimization problem our results extend for example the recent result of v colao g marino h k xu an iterative method for finding common solutions of equilibrium and fixed point problems j math anal appl 344 2008 340 352 to systems of equilibrium problems

strong convergence theorems for a new iterative method of k strictly pseudo contractive mappings in hilbert spaces in this paper we introduce a new iterative method of a k strictly pseudo contractive mapping for some email protected k 1 and prove that the sequence x n converges strongly to a fixed point of t which solves a variational inequality related to the linear operator a our results have extended and improved the corresponding results of y j cho s m kang and x qin some results on k strictly pseudo contractive mappings in hilbert spaces nonlinear anal 70 2008 1956 1964 and many others

hybrid pseudo viscosity approximation schemes for systems of equilibrium problems and fixed point problems of infinite family and semigroup of non expansive mappings abstract in this paper we introduce hybrid pseudo viscosity approximation schemes with strongly positive bounded linear operators for finding a common element of the set of solutions to a system of equilibrium problems the set of fixed points of an infinite family and left amenable semigroup of non expansive mappings in the frame work of hilbert spaces our goal is to prove a result of strong convergence for hybrid pseudo viscosity approximation schemes to approach a solution of systems of equilibrium problems which is also a common fixed point of an infinite family and left amenable semigroup of non expansive mappings the results presented in this paper can be treated as an extension and improvement of the corresponding results announced by ceng et al l c ceng q h ansari and j c yao hybrid pseudo viscosity approximation schemes for equilibrium problems and fixed point problems of infinitely many non expansive mappings nonlinear analysis 4 2010 743 754 and many others

tensor powers of modules over finitely generated abelian groups in an earlier paper 11 the authors investigated as a major component of their final result a special case of the following question let r be a commutative ring with unity g a finitely generated abelian group and a4 a finitely generated rg module consider the tensor power m as an rg module via the diagonal action of g under what conditions is m a finitely generated rg module the answer obtained in 1 was for the case when r is a field and used an invariant z m introduced by the first author and strebel in 3 we briefly describe cl firstly if n is the torsion free rank of g we can identify hom g w with w defining two elements of hom g iw to be equivalent if they differ by a positive real multiple we obtain a natural projection of hom g w o onto the sphere s i denote the equivalence class of xe hom g 1w by x and define gcxi g ge g x g 30 then z is the subset of s consisting of all those x for which m is a finitely generated rg module and cl is the complement of c in s we say that m is k tame if there do not exist x i xk in zh such that x1 xk 0 then the partial answer referred to above theorem 3 4 of l is

local regularity and decay estimates of solitary waves for the rotation modified kadomtsev petviashvili equation this paper is mainly concerned with the local low regularity of solutions and decay estimates of solitary waves to the rotation modified kadomtsevpetviashvili rmkp equation it is shown that with negative dispersion the rmkp equation is locally well posed for data in hs1 s2 r2 for s1 13 and s2 0 and hence globally well posed in the space l2 moreover an improved result on the decay property of the solitary waves is established which shows that all solitary waves of the rmkp equation decay exponentially at infinity

global well posedness for the kp i equation we prove the global well posedness of the kp i equation in bbb r 2 for data of arbitrary size in a suitable sobolev class we use a compactness method to get local solutions we extend the solutions thanks to some conservation laws an almost conserved quantity and strichartz estimates

viscosity approximation methods for equilibrium problems and fixed point problems in hilbert spaces abstract in this paper we introduce an iterative scheme by the viscosity approximation method for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a nonexpansive mapping in a hilbert space then we prove a strong convergence theorem which is connected with combettes and hirstoaga s result p l combettes s a hirstoaga equilibrium programming in hilbert spaces j nonlinear convex anal 6 2005 117 136 and wittmann s result r wittmann approximation of fixed points of nonexpansive mappings arch math 58 1992 486 491 using this result we obtain two corollaries which improve and extend their results

low regularity for the fifth order kadomtsev petviashvili i type equation abstract the cauchy problem of the fifth order kadomtsev petviashvili i equation fifth kp i 0 1 t u x 5 u x 3 u x 1 y y u x u 2 0 x y t r 3 is considered it follows that the fifth order kadomtsev petviashvili i equation 0 1 is locally well posed in h s 0 with s 3 4 where the norm h s r is defined by f h x y s r s r f l 2

equilibrium programming using proximal like algorithms we compute constrained equilibria satisfying an optimality condition important examples include convex programming saddle problems noncooperative games and variational inequalities under a monotonicity hypothesis we show that equilibrium solutions can be found via iterative convex minimization in the main algorithm each stage of computation requires two proximal steps possibly using bregman functions one step serves to predict the next point the other helps to correct the new prediction to enhance practical applicability we tolerate numerical errors

strong convergence for a minimization problem on solutions of systems of equilibrium problems and common fixed points of an infinite family and semigroup of nonexpansive mappings in this paper we introduce a suitable mann type algorithm for finding a common element of the set of solutions of systems of equilibrium problems and the set of common fixed points of an infinite family and left amenable semigroup of nonexpansive mappings in hilbert spaces then we prove the strong convergence of the proposed iterative scheme to the unique solution of the minimization problem on the solution of systems of equilibrium problems and the common fixed points of an infinite family and left amenable semigroup of nonexpansive mappings our results extend and improve the recent result of colao and marino v colao and g marino strong convergence for a minimization problem on points of equilibrium and common fixed points of an infinite family of nonexpansive mappings nonlinear anal 73 2010 3513 3524 and many others

convergence theorems of common elements for equilibrium problems and fixed point problems in banach spaces the purpose of this paper is to introduce hybrid projection algorithms for finding a common element of the set of common fixed points of two quasi f nonexpansive mappings and the set of solutions of an equilibrium problem in the framework of banach spaces our results improve and extend the corresponding results announced by many others

mixed equilibrium problems and optimization problems in this paper we introduce and analyze a new hybrid iterative algorithm for finding a common element of the set of solutions of mixed equilibrium problems and the set of fixed points of an infinite family of nonexpansive mappings furthermore we prove some strong convergence theorems for the hybrid iterative algorithm under some mild conditions we also discuss some special cases results obtained in this paper improve the previously known results in this area

strong convergence of a new composite iterative method for equilibrium problems and fixed point problems in this paper we propose a new composite iterative method for finding a common point of the set of solutions of an equilibrium problem and the set of fixed points of a countable family of nonexpansive mappings in a hilbert space it is proved that the sequence generated by the iterative scheme converges strongly to a common point of the set of solutions of an equilibrium problem and the set of fixed points of a countable family of nonexpansive mappings our results improve and extend the corresponding ones announced by many others

on a problem of bousfield for metabelian groups abstract the homological properties of localizations and completions of metabelian groups are studied it is shown that for r q or r z n and a finitely presented metabelian group g the natural map from g to its r completion induces an epimorphism of homology groups h 2 r this answers a problem of a k bousfield for the class of metabelian groups

a general iterative method for a finite family of nonexpansive mappings abstract we study the approximation of common fixed points of a finite family of nonexpansive mappings and suggest a modification of the iterative algorithm without the assumption of any type of commutativity also we show that the convergence of the proposed algorithm can be proved under some types of control conditions

iterative schemes for computing fixed points of nonexpansive mappings in banach spaces abstract let x be a real banach space with a normalized duality mapping uniformly norm to weak continuous on bounded sets or a reflexive banach space which admits a weakly continuous duality mapping j with gauge let f be an contraction and t n a sequence of nonexpansive mappings we study the strong convergence of explicit iterative schemes 1 x n 1 n f x n 1 n t n x n with a general theorem and then recover and improve some specific cases studied in the literature k aoyoma y kimura w takahashi m toyoda approximation of common fixed point of a countable family of nonexpansive mappings nonlinear anal 67 8 2007 2350 2360 g lopez v martin h k xu perturbation techniques for nonexpansive mappings with applications nonlinear anal real world appl in press available online 4 may 2008 h k xu viscosity approximation methods for nonexpansive mappings j math anal appl 298 1 2004 279 291 t h kim h k xu strong convergence of modified mann iterations nonlinear anal 61 1 2 2005 51 60 y song r chen strong convergence theorems on an iterative method for a family of finite nonexpansive mappings appl math comput 180 2006 275 287 y song r chen viscosity approximation methods for nonexpansive nonself mappings j math anal appl 321 1 2006 316 326 j chen l zhang t fan viscosity approximation methods for nonexpansive mappings and monotone mappings j math anal appl 334 2 2007 1450 1461 y kimura w takahashi m toyoda convergence to common fixed points of a finite family of nonexpansive mappings arch math 84 2005 350 363

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

cohomological finiteness conditions for elementary amenable groups it is proved that every elementary amenable group of type fp admits a cocompact classifying space for proper actions

iterative methods for common fixed points for a countable family of nonexpansive mappings in uniformly convex spaces abstract let e be a uniformly convex real banach space with a uniformly g teaux differentiable norm let k be a closed convex and nonempty subset of e let t i i 1 be a family of nonexpansive self mappings of k for arbitrary fixed 0 1 define a family of nonexpansive maps s i n 1 by s i 1 i t i where i is the identity map of k let f i 1 f t i 0 it is proved that an iterative sequence x n defined by x 0 k x n 1 n u i 1 i t n s i x n n 0 converges strongly to a common fixed point of the family t i i 1 where n and i t n are sequences in 0 1 satisfying appropriate conditions in each of the following cases a e l p 1 p and b at least one of the t i s is demicompact

nonexpansive retractions and nonlinear ergodic theorems in banach spaces on donne des theoremes ergodiques non lineaires pour des semigroupes commutatifs d applications non dilatation sans utiliser le concept de moyenne compacte

an explicit method for systems of equilibrium problems and fixed points of infinite family of nonexpansive mappings let h be a hilbert space t i i n a family of nonexpansive mappings from h into itself g i cxc r a finite family of equilibrium functions email protected 1 2 k a a strongly positive bounded linear operator with coefficient email protected and f an a contraction on h let w n be the mapping generated by t i and l n as in 1 5 let s r k n k be the resolvent generated by g k and r k n as in lemma 2 4 moreover let r k n k 1 k e n and l n satisfy appropriate conditions and email protected k 1 ksep g k n nfix t n email protected we introduce an explicit scheme which defines a suitable sequence as follows z n email protected email protected z n email protected na w ns r 1 n 1s r 2 n 2 s r k n kz email protected email protected n and z n strongly converges to x f which satisfies the variational inequality 0 for all email protected f the results presented in this paper mainly extend and improve some recent results in vittorio colao et al an implicit method for finding common solutions of variational inequalities and systems of equilibrium problems and fixed points of infinite family of nonexpansive mappings nonlinear anal 71 2009 2708 2715 s plubtieng r punpaeng a general iterative method for equilibrium problems and fixed point problems in hilbert spaces j math anal appl 336 2007 455 469 s takahashi w takahashi viscosity approximation methods for equilibrium problems and fixed point problems in hilbert spaces j math anal appl 331 2007 506 515

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

on the convergence of han s method for convex programming with quadratic objective we present an iterative method for minimizing strictly convex quadratic functions over the intersection of a finite number of convex sets the method consists in computing projections onto the individual sets simultaneously and the new iterate is a convex combination of those projections we give convergence proofs even for the inconsistent case i e when the intersection of the sets is empty

an implicit method for finding common solutions of variational inequalities and systems of equilibrium problems and fixed points of infinite family of nonexpansive mappings abstract let h be a hilbert space consider on h a sequence of nonexpansive mappings t n with common fixed points a finite family of equilibrium functions g i i 1 k a contraction f with coefficient 0 1 and a strongly positive linear bounded operator a with coefficient 0 let 0 assuming there are common equilibrium points of the family g i i 1 k which are also fixed points for t n we define a suitable sequence which strongly converges to the unique such point which also satisfies the variational inequality a f x x x 0 for all the x in the intersection of the equilibrium points and the common fixed points of the sequence t n