rational surface maps with invariant meromorphic two forms let f s dashrightarrow s be a rational self map of a smooth complex projective surface s and eta be a meromorphic two form on s satisfying f eta delta eta for some delta in mathbf c we show that under a mild topological assumption on f there is a birational change of domain psi x dashrightarrow s such that psi eta has no zeros in this context we investigate the notion of algebraic stability for f proving that f can be made algebraically stable if and only if it acts nicely on the poles of eta we illustrate this last result in the case eta frac dx wedge dy xy where we translate our stability result into a condition on whether a circle homeomorphism associated to f has rational rotation number

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

weak almost convergence theorem without opial s condition abstract let e be banach space with property u m m 1 r m n and a uniformly gateaux differentiable norm j e e a duality mapping d a nonempty closed convex bounded subset of e and t d d a uniformly l lipschitzian asymptotically hemicontractive mapping with l

fixed point theorem for generalized φ pseudocontractive mappings abstract let e be a real banach space c be a nonempty closed convex subset of e and t c c be a continuous generalized pseudocontractive mapping it is proved that t has a unique fixed point in c

strong convergence of modified mann iterations for a countable family of nonexpansive mappings abstract in this paper we propose a new modified mann iteration for computing common fixed points of nonexpansive mappings in a banach space we give certain different control conditions for the modified mann iteration then we prove strong convergence theorems for a countable family of nonexpansive mappings in uniformly smooth banach spaces these results improve and extend results of kim and xu t h kim h k xu strong convergence of modified mann iterations nonlinear anal 61 2005 51 60 yao et al y yao r chen and j yao strong convergence and certain control conditions for modified mann iteration nonlinear anal 68 2008 1687 1693 qin and su x qin y su approximation of a zero point of accretive operator in banach spaces j math anal appl 329 2007 415 424 and many others

iterative construction of fixed points of asymptotically nonexpansive mappings abstract let t be a completely continuous and asymptotically nonexpansive self mapping of a nonempty closed bounded and convex subset of a hilbert space then under certain conditions the sequence defined by xn 1 ntn xn 1 n x n converges strongly to some fixed point of t a similar result is obtained for asymptotically pseudocontractive mappings whose iterates are lipschitz continuous with respect to some common lipschitz constant

green currents for holomorphic automorphisms of compact kahler manifolds and some additional regularity properties very likely the currents t will describe the distribution of invariant manifolds of codimension s corresponding to the small est lyapounov exponents let dp denote the dynamical degree of order p of it describes the growth under iteration of the volume of p dimensional manifolds when d 1 it is natural to introduce first a positive closed 1 l current as ifnyoj 7 lim

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

strong convergence theorems for uniformly continuous pseudocontractive maps abstract let k be a nonempty closed convex subset of a real banach space e and let t k k be a uniformly continuous pseudocontraction fix any u k let x n be defined by the iterative process x 0 k x n 1 n n t x n 1 n x n 1 n u let denote the modulus of continuity of t with pseudo inverse if t t 0 t 1 and x n are bounded then under some mild conditions on the sequences n n and n n the strong convergence of x n to a fixed point of t is proved in the special case where t is lipschitz it is shown that the boundedness assumptions on t t 0 t 1 and x n can be dispensed with

dynamics of bimeromorphic maps of surfaces we classify bimeromorphic self maps f x inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i of compact kahler surfaces x in terms of their actions f h 1 1 x inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 02i on cohomology we observe that the growth rate of f n is invariant under bimeromorphic conjugacy and that by conjugating one can always arrange that f n f n we show that the sequence f n can be bounded grow linearly grow quadratically or grow exponentially in the first three cases we show that after conjugating f is an automorphism virtually isotopic to the identity f preserves a rational fibration or f preserves an elliptic fibration respectively in the last case we show that there is a unique up to scaling expanding eigenvector for f that is nef and that f is bimeromorphically conjugate to an automorphism if and only if 2 0 we go on in this case to construct a dynamically natural positive current representing and we study the growth rate of periodic orbits of f we conclude by illustrating our results with a particular family of examples

retracted a one step iterative process for two multivalued nonexpansive mappings in banach spaces weak and strong convergence a b s t r a c t in this paper we introduce a new one step iterative process to compute the common fixed points of two multivalued nonexpansive mappings furthermore we also prove some strong and weak convergence theorems in uniformly convex banach spaces

on the dynamics near infinity of some polynomial mappings in we construct the green current for a random iteration of horizontal like mappings in open image in new window this is applied to the study of a polynomial map open image in new window with the following properties

iterative solution of nonlinear equations involving set valued uniformly accretive operators abstract let e be a real normed linear space and let a e 2 e be a uniformly continuous and uniformly quasi accretive multivalued map with nonempty closed values such that the range of i a is bounded and the inclusion f ax has a solution x e it is proved that ishikawa and mann type iteration processes converge strongly to x further if t e 2 e is a uniformly continuous and uniformly hemicontractive set valued map with bounded range and a fixed point x e it is proved that both the mann and ishikawa type iteration processes converge strongly to x the strong convergence of these iteration processes with errors is also proved

strong convergence of an iterative method for nonexpansive and accretive operators abstract let x be a banach space and a an m accretive operator with a zero consider the iterative method that generates the sequence x n by the algorithm x n 1 n u 1 n j r n x n where n and r n are two sequences satisfying certain conditions and j r denotes the resolvent i r a 1 for r 0 strong convergence of the algorithm x n is proved assuming x either has a weakly continuous duality map or is uniformly smooth

discretely holomorphic parafermions and integrable loop models we define parafermionic observables in various lattice loop models including examples where no kramers wannier duality holds for a particular rhombic embedding of the lattice in the plane and a value of the parafermionic spin these variables are discretely holomorphic they satisfy a lattice version of the cauchy riemann equations as long as the boltzmann weights satisfy certain linear constraints in the cases considered the weights then also satisfy the critical yang baxter equations with the spectral parameter being related linearly to the angle of the elementary rhombus

critical and multicritical o n models soluble o n models on the square lattice are found via the yang baxter equations in a parameter space of three coupling constants a number of distinct soluble cases are found for each value of n some of these constitute critical or multicritical points in the phase diagram for all solutions the free energy per spin can be determined using the bethe ansatz by studying the finite size corrections at the critical points the critical exponents and the central charge can be found in some cases analytically and failing that numerically by extrapolation of exact results for finite size systems

dynamics of polynomial mappings of c 2 we study the dynamics of polynomial self mappings f of c 2 we construct for a large class of mappings an invariant measure which is mixing and of maximal entropy h f max log d t f log 1 f where d t f is the topological degree of f and 1 f its first dynamical degree to achieve this we look at the meromorphic extensions of f to smooth minimal compactifications of c 2 when a good compactification is found we construct an f invariant green current t which contains many dynamical informations when d t f 1 f 1 the measure is obtained as p dd c vt where v is a partial green function defined on the support of t when 1 t t where t is a globally defined f invariant current

existence theorems for m accretive operators in banach spaces abstract in 1985 the second author proved a surjective result for m accretive and expansive mappings for uniformly smooth banach spaces however in this case we have been able to remove the uniform smoothness of the banach space without any additional assumption

discretely holomorphic parafermions and integrable boundary conditions in two dimensional statistical models possessing a discretely holomorphic parafermion we introduce a modified discrete cauchy riemann equation on the boundary of the domain and we show that the solution of this equation yields integrable boundary boltzmann weights this approach is applied to i the square lattice o n loop model where the exact locations of the special and ordinary transitions are recovered and ii the fateev zamolodchikov spin model where a new rotation invariant integrable boundary condition is discovered for generic n

dynamical compactifications of c 2 we find good dynamical compactifications for arbitrary polynomial mappings of c 2 and use them to show that the degree growth sequence satisfies a linear integral recursion formula for maps of low topological degree we prove that the green function is well behaved for maps of maximum topological degree we give normal forms

discrete holomorphicity at two dimensional critical points after a brief review of the historical role of analyticity in the study of critical phenomena an account is given of recent discoveries of discretely holomorphic observables in critical two dimensional lattice models these are objects whose correlation functions satisfy a discrete version of the cauchy riemann relations their existence appears to have a deep relation with the integrability of the model and they are presumably the lattice versions of the truly holomorphic observables appearing in the conformal field theory cft describing the continuum limit this hypothesis sheds light on the connection between cft and integrability and if verified can also be used to prove that the scaling limit of certain discrete curves in these models is described by schramm loewner evolution sle

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

invariant approximations and r subweakly commuting maps the existence of invariant approximations for r subweakly commuting mappings is proved our results extend most of the known results to a new class of noncommuting mappings

henon like mappings in c we study the dynamics of a class of nonalgebraic holomorphic diffeomorphisms topo logical analogues in the unit bidisk of complex h6non mappings in c2 in particular a dynamical degree is defined which is related to topological entropy and we construct stable unstable invariant currents and prove there is a unique mixing measure of maximal entropy with product structure 1 introduction one of the most famous 2 dimensional dynamical systems is smale s horseshoe it is a basic example of a simple map with complicated dynamics and has served as a guideline for the whole modern development of discrete time dynamical systems a very natural problem in this context is to understand the dynamical phenomena occuring when uniform hyperbolicity of the horseshoe degenerates this was a motivation for the study of the so called henon map

solving variational inequalities involving nonexpansive type mappings abstract the purpose of this paper is to investigate the asymptotic behavior of algorithms for finding solutions for a certain class of variational inequalities v i d c i f involving nonexpansive type mappings in smooth banach spaces we study the existence of solutions of variational inequalities v i d c i f when d is the set of solutions of zeros of accretive operators or the set of fixed points of nonexpansive mappings or the set of fixed points of pseudocontractive mappings our convergence analysis covers proximal point algorithm for finding zeros of accretive operators as well as functional halpern algorithm for finding fixed points of nonexpansive mappings in banach spaces our results improve a number of results concerned with viscosity approximation methods in the context of weakly contraction mappings

the analysis of partial differential operators i hormander springer 1985 vol 1 391 pp vol 2 390 pp vol 3 525 pp vol 4 351 pp

regularity of dynamical green s functions for meromorphic maps of complex manifolds ergodic theory and pluripotential theory are closely related in nice enough situations dynamically defined green s functions give rise to invariant currents which intersect to yield measures of maximal entropy nice enough is often a condition on the regularity of the green s function in this paper we look at a variety of regularity properties that have been considered for dynamical green s functions we simplify and extend some known results and prove several others which are new we also give some examples indicating the limits of what one can hope to achieve in complex dynamics by relying solely on the regularity of a dynamical green s function

convergence of composite iterative methods for finding zeros of accretive operators abstract strong convergence theorems on composite iterative schemes by the viscosity approximation methods for finding a zero of an accretive operator are established in banach spaces the main results generalize the recent corresponding results of aoyama et al k aoyama y kimura w takahashi m toyoda approximation of common fixed points of a countable family of nonexpansive mappings in banach spaces nonlinear anal 67 2007 2350 2360 ceng et al l c ceng a r khan q h ansari j c yao strong convergence of composite iterative schemes for zeros of m accretive operators in banach spaces nonlinear anal 70 2009 1830 1840 kim and xu t h kim h k xu strong convergence of modified mann iterations nonlinear anal 61 2005 51 60 and xu h k xu strong convergence of an iterative method for nonexpansive and accretive operators j math anal appl 314 2006 631 643 to viscosity methods in a strictly convex and reflexive banach space having a uniformly g teaux differentiable norm our results also improve the corresponding results of t d benavides g l acedo h k xu iterative solutions for zeros of accretive operators math nachr 248 249 2003 62 71 r chen z zhu viscosity approximation fixed points for nonexpansive and m accretive operators fixed point theory appl 2006 2006 1 10 s kamimura w takahashi approximation solutions of maximal monotone operators in hilbert spaces j approx theory 106 2000 226 240 p e mainge viscosity methods for zeroes of accretive operators j approx theory 140 2 2006 127 140 k nakajo strong convergence to zeros of accretive operators in banach spaces j nonlinear convex anal 7 2006 71 81

strong convergence theorems for multivalued nonexpansive nonself mappings in banach spaces abstract let e be a uniformly convex banach space with a uniformly g teaux differentiable norm c a nonempty closed convex subset of e and t c k e a nonexpansive mapping for u c and t 0 1 let x t be a fixed point of a contraction g t c k e defined by g t x t t x 1 t u x c it is proved that if c is a nonexpansive retract of e x t is bounded and t z z for any fixed point z of t then the strong lim t 1 x t exists and belongs to the fixed point set of t furthermore we study the strong convergence of x t with the weak inwardness condition on t in a reflexive banach space with a uniformly g teaux differentiable norm

strong convergence theorems for nonexpansive semigroup in banach spaces abstract let k be a nonempty closed convex subset of a reflexive and strictly convex banach space e with a uniformly g teaux differentiable norm and f t t t 0 a nonexpansive self mappings semigroup of k and f k k a fixed contractive mapping the strongly convergent theorems of the following implicit and explicit viscosity iterative schemes x n are proved x n n f x n 1 n t t n x n x n 1 n f x n 1 n t t n x n and the cluster point of x n is the unique solution to some co variational inequality

semigroups generated by pseudo contractive mappings under the nagumo condition let x be a banach space whose dual space x is uniformly convex we demonstrate that for any demicontinuous weakly nagumo k pseudo contractive mapping t d t x x with closed domain a t i weakly generates a semigroup on d t in this paper we project the consequences of this result on fixed point theory in particular we show that if k 1 id est if t is strongly pseudo contractive then t has a unique fixed point this implies that if t is pseudo contractive k 1 and d t is closed bounded and convex then t has at least one fixed point consequently any demicontinuous pseudo contractive mapping t c c for an appropriate c has a fixed point which has been an important open question in fixed point theory for quite some time in a subsequent paper we explore the consequences of the semigroup result on the existence of solutions to certain partial differential equations the semigroup result directly implies the existence of unique global solutions to time evolution equations of the form u au where a is a combination of derivatives the fixed point results from this paper imply the existence of solutions to partial differential equations of the form lu f

ergodic properties of rational mappings with large topological degree let x be a projective manifold and f x x a rational mapping with large topological degree dt ek 1 f the k 1 th dynamical degree of f we give an elementary construction of a probability measure ef such that d n t fn ef for every smooth probability measure on x we show that every quasiplurisubharmonic function is ef integrable in particular ef does not charge either points of indeterminacy or pluripolar sets hence ef is f invariant with constant jacobian f ef dt ef we then establish the main ergodic properties of ef it is mixing with positive lyapunov exponents preimages of hmost h points as well as repelling periodic points are equidistributed with respect to ef moreover when dimc x 3 or when x is complex homogeneous ef is the unique measure of maximal entropy

iterative algorithm for multi valued pseudocontractive mappings in banach spaces abstract let d be nonempty open convex subset of a real banach space e let t d k c e be a continuous pseudocontractive mapping satisfying the weakly inward condition and let u d be fixed then for each t 0 1 there exists y t d satisfying y t t t y t 1 t u if in addition e is reflexive and has a uniformly g teaux differentiable norm and is such that every closed convex bounded subset of d has fixed point property for nonexpansive self mappings then t has a fixed point if and only if y t remains bounded as t 1 in this case y t converges strongly to a fixed point of t as t 1 moreover an explicit iteration process which converges strongly to a fixed point of t is constructed in the case that t is also lipschitzian

conformal invariance of spin correlations in the planar ising model we rigorously prove the existence and the conformal invariance of scaling limits of the magnetization and multi point spin correlations in the critical ising model on arbitrary simply connected planar domains this solves a number of conjectures coming from the physical and the mathematical literature the proof relies on convergence results for discrete holomorphic spinor observables and probabilistic techniques

equivalent theorems of the convergence between proximal type algorithms abstract the main aim of this work is to give the equivalence of the convergence between proximal type algorithms our convergence analysis covers rockafellar type proximal point algorithm with a weak contraction for finding zeros of accretive operators as well as browder and halpern type iterations and viscosity approximation methods for finding fixed points of nonexpansive type mappings in banach spaces we also provide simple proofs of some results of wong sahu and yao n c wong d r sahu j c yao solving variational inequalities involving nonexpansive type mappings nonlinear anal 69 12 2008 4732 4753

scaling dimensions and conformal anomaly in anisotropic lattice spin models the effect of anisotropic interactions on the eigenvalue spectrum of the row to row transfer matrix of critical lattice spin models is investigated it is verified that the predictions of conformal theory apply to anisotropic systems if one allows for spatial rescaling by incorporating an anisotropy factor zeta ay ax sin theta where ay and ax are lattice spacings and theta is an angle describing the anisotropy for exactly solvable models these anisotropy angles can be calculated analytically using corner transfer matrices this is done for the eight vertex model hard hexagons and interacting hard squares and it is found that theta pi u lambda 10u 3 and 5u respectively where u is the spectral parameter and lambda is the crossing parameter for each of these models the amplitude of the finite size corrections to the free energy at criticality is found to be of the form pi zeta c 6n2 where zeta is the anisotropy factor and the central charge or conformal anomaly is given by c 1 4 5 and 7 10 respectively this is an analytic result for the eight vertex model for the hard hexagon and square models the largest eigenvalues are found accurately by numerically solving their inversion identities for various anisotropies and strip widths up to n 48 finally the authors argue that the anisotropy angle for magnetic hard squares and the q state potts models is also given by theta pi u lambda so this result is quite general

strong convergence theorems for a common zero of a finite family of m accretive mappings suppose k is a closed convex subset of a strictly convex real banach space e which has a uniformly g teaux differentiable norm suppose that every nonempty closed convex bounded subset of e has the fixed point property for nonexpansive mappings a strong convergence theorem is proved for a common zero of a family of m accretive mappings from k to e as a consequence an iterative method is constructed to converge to a common fixed point assuming existence of a family of pseudocontractive mappings from k to e under certain mild condition

strong convergence of iterative methods by strictly pseudocontractive mappings in banach spaces abstract in this paper we deal with fixed point computational problems by strongly convergent methods involving strictly pseudocontractive mappings in smooth banach spaces first we prove that the s iteration process recently introduced by sahu in 14 converges strongly to a unique fixed point of a mapping t where t is strongly pseudocontractive mapping from a nonempty closed and convex subset c of a smooth banach space into itself it is also shown that the hybrid steepest descent method converges strongly to a unique solution of a variational inequality problem with respect to a finite family of i strictly pseudocontractive mappings from c into itself our results extend and improve some very recent theorems in fixed point theory and variational inequality problems particularly the results presented here extend some theorems of reich 1980 1 and yamada 2001 15 to a general class of strictly pseudocontractive mappings in uniformly smooth banach spaces

strong convergence theorems for accretive operators in banach spaces abstract let e be a reflexive banach space with a uniformly g teaux differentiable norm and let a e e be m accretive assume that s cl d a e is bounded strongly accretive and continuous for x e and t 0 let xt be the unique solution of the inclusion x sxt taxt it is proved that if there exists a nonexpansive retraction p of e onto cl d a then the strong limt 0xt exists moreover it is shown that if every weakly compact convex subset of e has the fixed point property for nonexpansive mappings and 0 r a then the strong limt xt exists and belongs to a 10 an interesting application to a convergence result for an implicit iterative scheme is also included

convergences of nonexpansive iteration processes in banach spaces abstract let e be a reflexive banach space with a uniformly g teaux differentiable norm and s be a mapping of the form s 0 i 1 t 1 2 t 2 k t k where i 0 0 0 i 0k i 1 and t i e e i 1 2 k is a nonexpansive mapping for an arbitrary x0 e let xn be a sequence in e defined by an iteration xn 1 sxn n 0 1 2 we establish a dual weak almost convergence result of xn in a reflexive banach space with a uniformly g teaux differentiable norm as a consequence of the result a weak convergence result of xn is also given

a unified hybrid iterative method for solving variational inequalities involving generalized pseudocontractive mappings we study in this paper the existence and the approximation of solutions of variational inequalities involving generalized pseudocontractive mappings in banach spaces the convergence analysis of a proposed hybrid iterative method for approximating common zeros or fixed points of a possibly infinitely countable or uncountable family of such operators will be conducted within the conceptual framework of the viscosity approximation technique in reflexive banach spaces with uniform g teaux differentiable norms this technique should make existing or new results in solving variational inequalities more applicable

real and complex dynamics of a family of birational maps of the plane the golden mean subshift we describe the real dynamics of a family of birational mappings of the plane by combining complex intersection theory and techniques from smooth dynamical systems we are able to give an essentially complete account of the behavior of both wandering and nonwandering orbits in particular the golden mean subshift provides a topological model for the dynamics on the nonwandering set while the mappings are not hyperbolic they are shown to possess many of the structures associated with hyperbolicity

variational inequalities for φ pseudo contractive mappings abstract usually results on strongly accretive operators involve various assumptions on the function such as continuity being positive and or being strictly increasing however by redefining this function we are able to eliminate all these additional assumptions and leave only the positiveness condition t 0 for t 0 this fact allows us to extend a theorem of deimling and obtain a general result for the solvability of a variational inequality for strongly pseudo contractive mappings

rhombic embeddings of planar quad graphs given a finite or infinite planar graph all of whose faces have degree 4 we study embeddings in the plane in which all edges have length 1 that is in which every face is a rhombus we give a necessary and sucient condition for the existence of such an embedding as well as a description of the set of all such embeddings r etant donne un graphe planaire fini ou infini dont toutes les faces sont de degre 4 onetudie ses plongements dans le plan dont toutes les aretes sont de longueur 1 c estdire dont toutes les faces sont des losanges on donne une condition necessaire et susante pour l existence d un tel plongement et on decrit l ensemble de ces plongements

integrability as a consequence of discrete holomorphicity loop models it has recently been established that imposing the condition of discrete holomorphicity on a lattice parafermionic observable leads to the critical boltzmann weights in a number of lattice models remarkably the solutions of these linear equations also solve the yang baxter equations we extend this analysis for the zn model by explicitly considering the condition of discrete holomorphicity on two and three adjacent rhombi for two rhombi this leads to a quadratic equation in the boltzmann weights and for three rhombi a cubic equation the two rhombus equation implies the inversion relations the star triangle relation follows from the three rhombus equation we also show that these weights are self dual as a consequence of discrete holomorphicity this article is part of lattice models and integrability a special issue of journal of physics a mathematical and theoretical in honour of f y wu s 80th birthday

best simultaneous approximations asymptotically nonexpansive mappings and variational inequalities in banach spaces abstract the existence of common fixed points is established for three mappings where t is either generalized f g nonexpansive or asymptotically f g nonexpansive on a nonempty subset of a banach space as applications the invariant best simultaneous approximation results are proved and the existence of solution of variational inequalities is obtained our results unify and substantially improve several recent results existing in the current literature

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

viscosity approximation methods for a family of finite nonexpansive mappings in banach spaces viscosity approximation methods for a family of finite nonexpansive mappings are established in banach spaces the main theorems extend the main results of moudafi viscosity approximation methods for fixed points problems j math anal appl 241 2000 46 55 and xu viscosity approximation methods for nonexpansive mappings j math anal appl 298 2004 279 291 to the case of finite mappings our results also improve and unify the corresponding results of bauschke the approximation of fixed points of compositions of nonexpansive mappings in hilbert space j math anal appl 202 1996 150 159 browder convergence of approximations to fixed points of nonexpansive mappings in banach spaces archiv ration mech anal 24 1967 82 90 cho et al some control conditions on iterative methods commun appl nonlinear anal 12 2 2005 27 34 ha and jung strong convergence theorems for accretive operators in banach spaces j math anal appl 147 1990 330 339 halpern fixed points of nonexpansive maps bull amer math soc 73 1967 957 961 jung iterative approaches to common fixed points of nonexpansive mappings in banach spaces j math anal appl 302 2005 509 520 jung et al iterative schemes with some control conditions for a family of finite nonexpansive mappings in banach space fixed point theory appl 2005 2 2005 125 135 jung and kim convergence of approximate sequences for compositions of nonexpansive mappings in banach spaces bull korean math soc 34 1 1997 93 102 lions approximation de points fixes de contractions c r acad sci ser a b paris 284 1977 1357 1359 o hara et al iterative approaches to finding nearest common fixed points of nonexpansive mappings in hilbert spaces nonlinear anal 54 2003 1417 1426 reich strong convergence theorems for resolvents of accretive operators in banach spaces j math anal appl 75 1980 287 292 shioji and takahashi strong convergence of approximated sequences for nonexpansive mappings in banach spaces proc amer math soc 125 12 1997 3641 3645 takahashi and ueda on reich s strong convergence theorems for resolvents of accretive operators j math anal appl 104 1984 546 553 wittmann approximation of fixed points of nonexpansive mappings arch math 59 1992 486 491 xu iterative algorithms for nonlinear operators j london math soc 66 2 2002 240 256 and zhou et al strong convergence theorems on an iterative method for a family nonexpansive mappings in reflexive banach spaces appl math comput in press among others

iterative approximation to common fixed points of nonexpansive mapping sequences in reflexive banach spaces abstract let e be a real reflexive banach space which admits a weakly sequentially continuous duality mapping from e to e and k be a nonempty closed convex subset of e suppose that t n n 1 2 is a uniformly asymptotically regular sequence of nonexpansive mappings from k into itself such that f n 1 f t n 0 for arbitrary initial value x 0 k and fixed contractive mapping f k k define iteratively a sequence x n as follows x n 1 n 1 f x n 1 n 1 t n 1 x n n 0 where n 0 1 satisfies lim n n 0 and n 1 n we prove that x n converges strongly to p f as n where p is the unique solution in f to the following variational inequality i f p j p u 0 for all u f t our results extend and improve the corresponding ones given by o hara et al j g o hara p pillay h k xu iterative approaches to finding nearest common fixed point of nonexpansive mappings in hilbert spaces nonlinear anal 54 2003 1417 1426 j s jung iterative approaches to common fixed points of nonexpansive mappings in banach spaces j math anal appl 302 2005 509 520 h k xu viscosity approximation methods for nonexpansive mappings j math anal appl 298 2004 279 291 and o hara et al j g o hara p pillay h k xu iterative approaches to convex feasibility problem in banach space nonlinear anal available online 20 october 2005 doi 10 1016 j na 2005 07 36

a new alternating direction method for solving variational inequalities we introduce a modified alternating direction method for structured monotone variational inequalities by performing an additional projection step at each iteration and another optimal step length is employed to reach substantial progress in each iteration this method only needs functional values for given variables in the solution process and avoids the task of estimating the co coercive modulus all the computing process are easily implemented and the global convergence is also presented under mild assumptions some preliminary computational results are given

on reich s strong convergence theorems for resolvents of accretive operators let e be a real banach space with norm i then an operator a c e x e with domain d a and range r a is said to be accretive if xi xz 0 an accretive operator a c e x e is m accretive if r i ra e for all r 0 where z is the identity if a is accretive we can define for each positive r a singlevalued mapping j r z ra d a by j z ra it is called the resolvent of a in 6 reich proved the following theorem let e be a uniformly smooth banach space and let a c e x e be m accretive if 0 e r a then for each x in e the strong lim z x exists and belongs to a io he remarked also that the assumption that a is m accretive can be replaced with the assumption that cl a the closure of d a is convex and that a satisfies the range condition r z ra 1 cl d a for all r 0 in this paper we first prove a theorem that generalizes simultaneously the above results furthermore we generalize another reich strong convergence theorem asserting that the strong lim z x exists in uniformly convex and uniformly smooth banach spaces though our proofs are similar to those in 6 they are slightly simple on account of using banach limits

the energy density in the planar ising model we study the critical ising model on the square lattice in bounded simply connected domains with and free boundary conditions we relate the energy density of the model to a discrete fermionic spinor and compute its scaling limit by discrete complex analysis methods as a consequence we obtain a simple exact formula for the scaling limit of the energy field one point function in terms of the hyperbolic metric this confirms the predictions originating in physics but also provides a higher precision

on kirk s strong convergence theorem for multivalued nonexpansive mappings on cat 0 spaces abstract we prove a strong convergence theorem for multivalued nonexpansive mappings which includes kirk s convergence theorem on cat 0 spaces the theorem properly contains a result of jung for hilbert spaces we then apply the result to approximate a common fixed point of a countable family of single valued nonexpansive mappings and a compact valued nonexpansive mapping

universality in the 2d ising model and conformal invariance of fermionic observables it is widely believed that the celebrated 2d ising model at criticality has a universal and conformally invariant scaling limit which is used in deriving many of its properties however no mathematical proof has ever been given and even physics arguments support a priori weaker mobius invariance we introduce discrete holomorphic fermions for the 2d ising model at criticality on a large family of planar graphs we show that on bounded domains with appropriate boundary conditions those have universal and conformally invariant scaling limits thus proving the universality and conformal invariance conjectures

the mann process for perturbed m accretive operators in banach spaces this work was carried out while this author was visiting the university ofalabama in huntsville underthe nancial support by the lg yonam foundation 1998 and he would like to thank professor claudio h morales for his hospitality in the department of mathematics 0362 546x 01 see front matter 2001 elsevier science ltd all rights reserved pii s0362 546x 00 00115 2

approximation of fixed points of uniformly r subweakly commuting mappings we introduce a new class of uniformly r subweakly commuting mappings and then using this class study the problem of approximation of common fixed points of asymptotically s nonexpansive mappings in a banach space with uniformly g teaux differentiable norm

energy and invariant measures for birational surface maps given a birational self map of a compact complex surface it is useful to find an invariant measure that relates the dynamics of the map to its action on cohomology under a very weak hypothesis on the map we show how to construct such a measure the main point in the construction is to make sense of the wedge product of two positive closed 1 1 currents we are able to do this in our case because local potentials for each current have finite energy with respect to the other our methods also suffice to show that the resulting measure is mixing does not charge curves and has nonzero lyapunov exponents

on viscosity iterative methods for variational inequalities abstract let j be a commutative family of nonexpansive mappings of a closed convex subset c of a reflexive banach space x such that the set of common fixed point is nonempty in this paper we suggest and analyze a new viscosity iterative method for a commutative family of nonexpansive mappings we also prove that the approximate solution obtained by the proposed method converges to a solution of a variational inequality our method of proof is simple and different from the other methods results proved in this paper may be viewed as an improvement and refinement of the previously known results

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

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

geometric properties of upper level sets of lelong numbers on projective spaces let t be a positive closed current of unit mass on the complex projective space mathbb p n for certain values alpha 1 we prove geometric properties of the set of points in mathbb p n where the lelong number of t exceeds alpha we also consider the case of positive closed currents of bidimension 1 1 on multiprojective spaces

conserved currents in the six vertex and trigonometric solid on solid models we construct quasi local conserved currents in the six vertex model with anisotropy parameter by making use of the quantum group approach of bernard and felder from these currents we construct parafermionic operators with spin that obey a discrete integral condition around lattice plaquettes embedded into the complex plane these operators are identified with primary fields in a c 1 compactified free boson conformal field theory we then consider a vertex face correspondence that takes the six vertex model to a trigonometric sos model and construct sos operators that are the image of the six vertex currents under this correspondence we define corresponding sos parafermionic operators with spins s 1 and that obey discrete integral conditions around sos plaquettes embedded into the complex plane we consider in detail the cyclic sos case corresponding to the choice with coprime we identify our sos parafermionic operators in terms of the screening operators and primary fields of the associated conformal field theory

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