a new iterative algorithm for common solutions of a finite family of accretive operators abstract the purpose in this paper is to prove a theorem of strong convergence to a common solution for a finite family of accretive operators in a strictly convex banach space by means of a new iterative algorithm which is a generalization and extension of the results of kim and xu t h kim h k xu strong convergence of modified mann iterations nonlinear anal 61 2005 51 60 and zegeye and shahzad h zegeye n shahzad strong convergence theorems for a common zero of a finite family of m accretive mappings nonlinear anal 66 2007 1161 1169 further using the result the theorem of strong convergence to a common fixed point is discussed for a finite family of pseudocontractive mappings under certain conditions

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

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

iterative approaches to convex feasibility problems in banach spaces abstract the convex feasibility problem cfp of finding a point in the nonempty intersection i 1 n c i is considered where n 1 is an integer and each c i is assumed to be the fixed point set of a nonexpansive mapping t i x x with x a banach space it is shown that the iterative scheme x n 1 n 1 y 1 n 1 t n 1 x n is strongly convergent to a solution of cfp provided the banach space x either is uniformly smooth or is reflexive and has a weakly continuous duality map and provided the sequence n satisfies certain conditions the limit of x n is located as q y where q is the sunny nonexpansive retraction from x onto the common fixed point set of the t i s

a dilute bootstrap percolation lattice model for unresponsiveness in t cell immunology the biased majority rule of cellular automata takes a spin up if and only if at least two of its four nearest neighbors on the square lattice are up we generalize this type of bootstrap percolation by introducing quenched site dilution as well as a random birth and decay process our monte carlo simulations then give first order transitions qualitatively similar to our results from meanfield reaction equations describing the induction of t cell unresponsiveness in the immune system

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

solutions of system of equilibrium and variational inequality problems on fixed points of infinite family of nonexpansive mappings in this paper we introduce a hybrid viscosity approximation scheme for finding a common element of the solution set for a system of equilibrium problems the solution set for a system of variational inequality problems and the common fixed point set for an infinite family of nonexpansive mappings in hilbert spaces then we prove the strong convergence of the proposed iterative scheme our results improve and extend the results announced by ceng and yao 2008 4

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

approximation methods for common fixed points for a countable family of nonexpansive mappings abstract let e l p or l p space 1 p 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 i 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 the 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 e l p 1 p and at least one of the maps t i s is demicompact our theorems extend the results of p mainge approximation methods for common fixed points of nonexpansive mappings in hilbert space j math anal appl 325 2007 469 479 from hilbert spaces to l p spaces 1 p

hybrid viscosity approximation schemes for equilibrium problems and fixed point problems of infinitely many nonexpansive mappings abstract recently takahashi and takahashi s takahashi w takahashi viscosity approximation methods for equilibrium problems and fixed point problems in hilbert spaces j math anal appl 2006 doi 10 1016 j jmaa 2006 08 036 suggested and analyzed 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 in this paper we introduce a new 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 common fixed points of infinitely many nonexpansive mappings in a hilbert space then we prove a strong convergence theorem which is the improvements and extension of takahashi and takahashi s 2006 corresponding result using this theorem we obtain two corollaries which improve and extend their corresponding results

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

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

generalized viscosity approximation methods for mixed equilibrium problems and fixed point problems in this paper we present a new iterative method based on the hybrid viscosity approximation method and the hybrid steepest descent method for finding a common element of the set of solutions of generalized mixed equilibrium problems and the set of common fixed points of a finite family of nonexpansive mappings in hilbert spaces furthermore we prove that the proposed iterative method has strong convergence under some mild conditions imposed on algorithm parameters the results presented in this paper improve and extend the corresponding results reported by some authors recently

an explicit method for finding common solutions of variational inequalities and systems of equilibrium problems and fixed points of an infinite family of nonexpansive mappings abstract let h be a hilbert space and c be a nonempty closed convex subset of h t i i n be a family of nonexpansive mappings from c into h g i c c r be a finite family of equilibrium functions i 1 2 k a be a strongly positive bounded linear operator with a coefficient and b lipschitzian relaxed cocoercive map of c into h moreover let r k n k 1 k n satisfy appropriate conditions and f k 1 k e p g k v i c b n n f i x t n 0 we introduce an explicit scheme which defines a suitable sequence as follows x n 1 n f x n 1 n a w n p c i s n b s r 1 n 1 s r 2 n 2 s r k n k x n n n and x n strongly converges to x f which satisfies the variational inequality a f x x x 0 for all x f the results presented in this paper mainly extend and improve a recent result of colao v colao 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 analysis 2009 doi 10 1016 j na 2009 01 115 and qin x qin m shang y su a general iterative method for equilibrium problems and fixed point problems in hilbert spaces nonlinear analysis 69 2008 3897 3909

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

an explanation of scale dependent dispersivity in heterogeneous aquifers using concepts of fractal geometry stochastic transport theories rely on the assumptions that the principles of stationarity and ergodicity are satisfied these assumptions imply that the pattern of heterogeneity can be viewed as being spatially periodic thus yielding a finite correlation scale we examine a type of heterogeneity which does not satisfy these principles self similar or fractal heterogeneity which exhibits a pattern over a large range of scales that is independent of the scale of observation and thus will possess a very large correlation scale we review the basic concepts of fractal geometry and develop scaling relationships for fractal travel distance versus scale of observation we then develop lagrangian models for dispersion in a single fractal streamtube and for a set or bundle of fractal streamtubes the results are compared to classical one dimensional advection dispersion theory existing fractal and stochastic theories and to a summary of field measured dispersivity data for the single streamtube model field measured dispersivity is proportional to the straight line travel distance raised to a power of d 1 where d is the fractal dimension for the set of fractal streamtubes field measured dispersivity is proportional to the straight line travel distance raised to a power of 2d 1 the analytical expressions are verified and elaborated by a fractal random walk computer model the computer model is used to show the self similar nature of heterogeneity that is independent of the scale of observation comparisons of the field dispersivity data with our fractal models indicate that most tracer tests have been performed in media that approximate a set of fractal streamtubes

strong convergence of the modified ishikawa iterative method for infinitely many nonexpansive mappings in banach spaces in this paper we introduce a new modified ishikawa iterative process for computing fixed points of an infinite family nonexpansive mapping in the framework of banach spaces then we establish the strong convergence theorem of the proposed iterative scheme under some mild conditions which solves a variational inequality the results obtained in this paper extend and improve on the recent results of qin et al strong convergence theorems for an infinite family of nonexpansive mappings in banach spaces journal of computational and applied mathematics 230 1 2009 121 127 cho et al approximation of common fixed points of an infinite family of nonexpansive mappings in banach spaces computers and mathematics with applications 56 2008 2058 2064 and many others

the set of common fixed points of an n parameter continuous semigroup of mappings abstract in this paper using kronecker s theorem we discuss the set of common fixed points of an n parameter continuous semigroup t p p r n of mappings we also discuss some convergence theorems to a common fixed point of an n parameter nonexpansive semigroup t p p r n without using the bochner integral

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

rigidity percolation in a field rigidity percolation with g degrees of freedom per site is analyzed on randomly diluted erdos renyi graphs with average connectivity gamma in the presence of a field h in the gamma h plane the rigid and flexible phases are separated by a line of first order transitions whose location is determined exactly this line ends at a critical point with classical critical exponents analytic expressions are given for the densities n f of uncanceled degrees of freedom and gamma r of redundant bonds upon crossing the coexistence line gamma r and n f are continuous although their first derivatives are discontinuous we extend for the case of nonzero field a recently proposed hypothesis namely that the density of uncanceled degrees of freedom is a free energy for rigidity percolation analytic expressions are obtained for the energy entropy and specific heat some analogies with a liquid vapor transition are discussed particularizing to zero field we find that the existence of a g 1 core is a necessary condition for rigidity percolation with g degrees of freedom at the transition point gamma c maxwell counting of degrees of freedom is exact on the rigid cluster and on the g 1 rigid core i e the average coordination of these subgraphs is exactly 2g although gamma c the average coordination of the whole system is smaller than 2g gamma c is found to converge to 2g for large g i e in this limit maxwell counting is exact globally as well

on modified iterative method for nonexpansive mappings and monotone mappings abstract in this paper we introduce a new iterative scheme for finding the common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality for inverse strongly monotone mappings we show that the sequence converges strongly to a common element of the above two sets under some parameters controlling conditions

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

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

approximation methods for common fixed points of infinite countable family of nonexpansive mappings let e be a real strictly convex and reflexive banach space with a uniformly gateaux differentiable norm and c be a nonempty closed convex subset of e consider the iterative sequence x n email protected n 1f x n email protected n email protected l n 1 w nx n where w n is the w mapping generated by an infinite countable family of nonexpansive mappings t n t n 1 t 1 and a n a n 1 a 1 such that the common fixed point sets email protected email protected n 1 f t n email protected and f c c is a given contractive mapping under very mild conditions on the parameters we prove that x n converges strongly to email protected f where p is the unique solution in f to the following variational inequality 0for all x f

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 of an iterative algorithm for an infinite family of strict pseudo contractions in banach spaces in this paper we introduce a new w mapping and present an iterative algorithm for an infinite family of strict pseudo contractions strong convergence theorems are proved in banach spaces our results improve and extend the corresponding result announced by cai and hu g cai c hu strong convergence theorems of modified ishikawa iterative process with errors for an infinite family of strict pseudo contractions nonlinear anal 71 12 2009 6044 6053

strong convergence theorems of modified ishikawa iterative process with errors for an infinite family of strict pseudo contractions abstract in this paper we study modified ishikawa iterative process with errors to have strong convergence for an infinite family of strict pseudo contractions in the framework of q uniformly smooth banach spaces our results improve and extend the recent ones announced by many others

viscosity approximation methods for generalized equilibrium problems and fixed point problems with applications abstract in this paper we introduce a general iterative scheme for finding a common element of the set of common solutions of generalized equilibrium problems the set of common fixed points of a family of infinite non expansive mappings strong convergence theorems are established in a real hilbert space under suitable conditions as some applications we consider convex feasibility problems and equilibrium problems the results presented improve and extend the corresponding results of many others

approximation of common fixed points of a countable family of nonexpansive mappings in a banach space in this paper to find a common fixed point of a family of nonexpansive mappings we introduce a halpern type iterative sequence then we prove that such a sequence converges strongly to a common fixed point of nonexpansive mappings moreover we apply our result to the problem of finding a common fixed point of a countable family of nonexpansive mappings and the problem of finding a zero of an accretive operator

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 of an iterative algorithm on an infinite countable family of nonexpansive mappings let c be a nonempty closed convex subset of a real strictly convex and reflexive banach space e which has a uniformly g teaux differentiable norm let f c c be a given contractive mapping and tn n 1 c c be an infinite family of nonexpansive mappings such that the common fixed point sets f n 1 f tn let n and n be two real sequences in 0 1 for given x0 c arbitrarily let the sequence xn be generated iteratively by xn 1 nf xn nxn 1 n n wnxn wherewn is the w mapping generated by the mappings tn tn 1 t1 and n n 1 1 suppose the iterative parameters n and n satisfy the following control conditions c1 limn n 0 c2 n 0 n b5 limsupn n 1 then the sequence xn converges strongly to p f where p is the unique solution in f to the following variational inequality i f p j p x 0for allx f

a new iterative method for equilibrium problems and fixed point problems of infinitely nonexpansive mappings and monotone mappings in this paper we introduce a new iterative scheme for finding the common element of the set of common fixed points of infinitely many nonexpansive mappings the set of solutions of an equilibrium problem and the set of solutions of the variational inequality for a inverse strongly monotone mapping in hilbert spaces we prove that the sequence converges strongly to a common element of the above three sets under some parameters controlling conditions this main result improve and extend plubtieng and punpaeng s corresponding result s plubtieng r punpaeng a new iterative method for equilibrium problems and fixed point problems of nonexpansive mappings and monotone mappings applied mathematics and computation 197 2008 548 558 using this theorem we obtain three corollaries

relaxed viscosity approximation methods for fixed point problems and variational inequality problems abstract let x be a real strictly convex and reflexive banach space with a uniformly g teaux differentiable norm and c be a nonempty closed convex subset of x let t n n 1 be a sequence of nonexpansive self mappings on c such that the common fixed point set f n 1 f t n 0 and f c c be a given contractive mapping and n be a sequence of nonnegative numbers in 0 1 consider the following relaxed viscosity approximation method x n 1 1 n n x n n f y n n w n y n y n 1 n x n n w n x n n 1 where w n is the w mapping generated by t n t n 1 t 1 and n n 1 1 for each n 1 it is proven that under very mild conditions on the parameters the sequence x n of approximate solutions generated by the proposed method converges strongly to some p f where p is the unique solution in f to the following variational inequality i f p j p x 0 x f

approximation theorems for solving common solution of a system of mixed equilibrium problems and variational inequality problems and fixed point problems for asymptotically strict pseudocontractions in the intermediate sense abstract in this paper we introduce a new iterative algorithm which is constructed by using the hybrid projection method for finding the common solution of a system of mixed equilibrium problems of bifunctions satisfying certain the conditions and the common solution of variational inequality problems of inverse strongly monotone mappings and the common solution of fixed point problems for a family of uniformly lipschitzian continuous and asymptotically i strict pseudocontractive mapping in the intermediate sense we prove the strong convergence theorem for a new iterative algorithm under some mild conditions in hilbert spaces finally we also give some numerical examples for support our results

finite size scaling behavior of a biased majority rule cellular automaton abstract we consider the biased majority rule cellular automaton in which the sites take the majority of the states 0 or 1 of their neighbors to update their states with a bias towards 1 in case of ties we observe that in any dimension for any initial density of 1 s the probability of final complete occupancy by 1 s converges to 1 as the lattice grows in two dimensions the value p l of the initial density for which the probability of eventual complete occupancy of a lattice l l is 0 1 is shown to satisfy for fixed the bounds a log l b log l for large l where a and b are positive and finite constants

strong convergence theorems for an infinite family of nonexpansive mappings in banach spaces in an infinite dimensional hilbert space the normal mann s iteration algorithm has only weak convergence in general even for nonexpansive mappings in order to get a strong convergence result we modify the normal mann s iterative process for an infinite family of nonexpansive mappings in the framework of banach spaces our results improve and extend the recent results announced by many others

approximation of common fixed points of an infinite family of nonexpansive mappings in banach spaces let c be a closed convex subset of a real uniformly smooth and strictly convex banach space e consider the following iterative algorithm given by x 0 x carbitrarily chosen y n b nx n 1 b n w nx n x n 1 a nf x n 1 a n y n n 0 where f is a contraction on c and w n is a mapping generated by an infinite family of nonexpansive mappings t i i 1 assume that the set of common fixed points of this infinite family of nonexpansive mappings is not empty in this paper we prove that the sequence x n generated by the above iterative algorithm converges strongly to a common fixed point of t i i 1 which solves some variational inequality our results improve and extend the results announced by many others

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

strong convergence theorems for finitely many nonexpansive mappings abstract under the assumption that e is a reflexive banach space whose norm is uniformly geteaux differentiable and which has a weakly continuous duality mapping j with gauge function ceng cubiotti yao strong convergence theorems for finitely many nonexpansive mappings and applications nonlinear analysis 67 2007 1464 1473 introduced a new iterative scheme for a finite commuting family of nonexpansive mappings and proved strong convergence theorems about this iteration in this paper only under the hypothesis that e is a reflexive banach space which has a weakly continuous duality mapping j with gauge function and several control conditions about the iterative coefficient are removed we present a short and simple proof of the above theorem

reply to comment on an explanation of scale dependent dispersivity in heterogeneous aquifers using concepts of fractal geometry by s w wheatcraft and s w tyler

a new iterative method for equilibrium problems and fixed point problems of nonexpansive mappings and monotone mappings abstract in this paper we introduce a new iterative scheme for finding the common element of the set of fixed points of a nonexpansive mapping the set of solutions of an equilibrium problem and the set of solutions of the variational inequality for inverse strongly monotone mappings we show that the sequence converges strongly to a common element of the above three sets under some parameters controlling conditions this main theorem extends a recent result of yao and yao y yao j c yao on modified iterative method for nonexpansive mappings and monotone mappings applied mathematics and computation 186 2 2007 1551 1558

strong convergence of an implicit iteration process for a finite family of nonexpansive mappings abstract the purpose of this paper is to prove the strong convergence of an implicit iteration process to a common fixed point for a finite family of nonexpansive mappings our theorems give an affirmative response to a question raised by xu and ori numer funct anal optim 22 2001 767 773

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 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

convergence theorems for strict pseudo contractions in q uniformly smooth banach spaces abstract in this paper we discuss some properties of iterates generated by a strict pseudo contraction or a finite family of strict pseudo contractions in a real q uniformly smooth banach space we prove the weak convergence and strong convergence of pseudo contractive mappings the results presented in this paper are interesting extensions and improvements upon those known ones of marino and xu g marino h k xu weak and strong convergence theorems for strict pseudo contractions in hilbert spaces j math anal appl 329 2007 336 349 acedo and xu g l acedo h k xu iterative methods for strict pseudo contractions in hilbert spaces nonlinear anal 67 2007 2258 2271 and zhou h zhou convergence theorems for strict pseudo contractions in 2 uniformly smooth banach spaces nonlinear anal 69 2008 3160 3173

an iterative algorithm for approximating convex minimization problem we suggest and analyze an iterative algorithm without the assumption of any type of commutativity on an infinite family of nonexpansive mappings we show that the proposed iterative algorithm converges to the unique minimizer of some quadratic function over the common fixed point sets of an infinite family of nonexpansive mappings our result extend and improve many results announced by many authors

convergence theorems of shrinking projection methods for equilibrium problem variational inequality problem and a finite family of relatively quasi nonexpansive mappings we introduce a w mapping for a finite family of relatively quasi nonexpansive mappings and construct an iterative scheme for finding a common element of the solution set of equilibrium problem the solution set of the variational inequality problem for an inverse strongly monotone operator and set of common fixed points of a finite family of relatively quasi nonexpansive mappings strong convergence theorems are presented in a 2 uniformly convex and uniformly smooth banach space our results generalize and extend relative results

characterizations of common fixed points of one parameter nonexpansive semigroups and convergence theorems to common fixed points we first prove characterizations of common fixed points of one parameter nonexpansive semigroups we next present convergence theorems to common fixed points

an extragradient like approximation method for variational inequality problems and fixed point problems the purpose of this paper is to investigate the problem of finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of a variational inequality problem for a monotone lipschitz continuous mapping we introduce an extragradient like approximation method which is based on so called extragradient method and viscosity approximation method we establish a strong convergence theorem for two iterative sequences generated by this method

on convergence of iteration processes for nonexpansive semigroups in uniformly convex and uniformly smooth banach spaces abstract let c be a closed bounded and convex subset of a uniformly convex and uniformly smooth banach space let t t t 0 be a strongly continuous nonexpansive semigroup on c consider the iterative process defined by the sequence of equations x k 1 c k t t k 1 x k 1 1 c k x k we prove that under certain conditions the sequence x k converges weakly to a common fixed point of the semigroup t t t 0 there are known results on convergence of such iterative processes for nonexpansive semigroups in hilbert spaces and banach spaces with the opial property however many important spaces like l p for 1 p 2 do not possess the opial property in this paper we do not assume the opial property we do assume instead that x is uniformly convex and uniformly smooth l p for p 1 are prime examples of such spaces

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

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 new method for solving equilibrium problem fixed point problem and variational inequality problem with application to optimization abstract in this paper we introduce a new iterative scheme for finding a common element of the set of solutions of an equilibrium problem the set of common fixed point for a family of infinitely nonexpansive mappings and the set of solutions of the variational inequality for inverse strongly monotone mappings in a hilbert space under suitable conditions some strong convergence theorems for approximating a common element of the above three sets are obtained as applications at the end of the paper we utilize our results to study the optimization problem and some convergence problem for strictly pseudocontractive mappings the results presented in the paper extend and improve some recent results of yao and yao y y yao j c yao on modified iterative method for nonexpansive mappings and monotone mappings appl math comput 186 2 2007 1551 1558 plubtieng and punpaeng s plubtieng r punpaeng a new iterative method for equilibrium problems and fixed point problems of nonlinear mappings and monotone mappings appl math comput 2007 doi 10 1016 j amc 2007 07 075 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 2006 506 515 su shang and qin y f su m j shang x l qin an iterative method of solution for equilibrium and optimization problems nonlinear anal 2007 doi 10 1016 j na 2007 08 045 and chang cho and kim s s chang y j cho j k kim approximation methods of solutions for equilibrium problem in hilbert spaces dynam systems appl in print

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

on relaxed viscosity iterative methods for variational inequalities in banach spaces in this paper we suggest and analyze a relaxed viscosity iterative method for a commutative family of nonexpansive self mappings defined on a nonempty closed convex subset of a reflexive banach space we prove that the sequence of approximate solutions generated by the proposed iterative algorithm converges strongly to a solution of a variational inequality our relaxed viscosity iterative method is an extension and variant form of the original viscosity iterative method the results of this paper can be viewed as an improvement and generalization of the previously known results that have appeared in the literature

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

a general iterative scheme for k strictly pseudo contractive mappings and optimization problems in this paper we introduce a new general iterative scheme for finding fixed points of a strictly pseudo contractive mapping and then prove that the sequence generated by the proposed iterative scheme converges strongly to a fixed point of the mapping which is a solution of a certain optimization problem related to a strongly positive bounded linear operator additional results of the main result are also obtained