on the steepest descent approximation method for the zeros of generalized accretive operators abstract in this paper we present certain characteristic conditions for the convergence of the generalized steepest descent approximation process to a zero of a generalized strongly accretive operator defined on a uniformly smooth banach space our study is based on an important result of reich s reich an iterative procedure for constructing zeros of accretive sets in banach spaces nonlinear anal 2 1978 85 92 and given results extend and improve some of the earlier results which include the steepest descent approximation method

convergence of three step iterations for asymptotically nonexpansive mappings in this paper weak and strong convergence theorems of three step iterations are established for asymptotically nonexpansive mappings in banach spaces the results obtained in this paper extend and improve the recent ones announced by xu and noor b l xu m a noor fixed point iterations for asymptotically nonexpansive mappings in banach spaces j math anal appl 267 2002 444 453 suthep suantai s suantai weak and strong convergence criteria of noor iterations for asymptotically nonexpansive mappings j math anal appl 311 2005 506 517 weerayuth nilsrakoo and satit saejung w nilsrakoo s saejung a new three step fixed point iteration scheme for asymptotically nonexpansive mappings appl math comput in press doi 10 1016 j amc 2006 01 063 and others

convergence to common fixed point of nonexpansive semigroups let e be a uniformly convex banach space whose norm is uniformly gateaux differentiable c be closed convex subset of e s t s s 0 be a nonexpansive semigroup on c such that the set of common fixed points of t s s 0 is nonempty let f c c be a contraction a n b n t n be real sequences such that 0 a n 0 lim n b n 0 and lim n t n y 0 c in this paper we show that the two iterative sequence as follows x n a nf x n 1 a n 1t n 0 t nt s x nds y n 1 b nf y n 1 b n 1t n 0 t nt s y ndsconverge strongly to a common fixed point of t s s 0 which solves some variational inequality when a n b n satisfy some appropriate conditions

strong convergence of an iterative algorithm for pseudocontractive mapping in banach spaces abstract let c be a nonempty closed convex subset of a real uniformly smooth banach space x t c c a pseudocontractive mapping let n n and n be three real sequences in 0 1 satisfying appropriate conditions then for fixed u c and arbitrary x 0 c the sequence x n generated by x n n u n x n 1 n t x n n 1 converges strongly to a fixed point of t

the coarse baum connes conjecture for spaces which admit a uniform embedding into hilbert space corollary 1 2 let be a finitely generated group if as a metric space with a word length metric admits a uniform embedding into hilbert space and its classifying space b has the homotopy type of a finite cw complex then the strong novikov conjecture holds for i e the index map from k b to k c r is injective corollary 1 2 follows from theorem 1 1 and the descent principle 23 by index theory the strong novikov conjecture implies the novikov conjecture on the homotopy invariance of higher signatures cf 8 for an excellent

convergence theorems of common fixed points for a finite family of lipschitz pseudocontractions in banach spaces abstract in this paper we continue to study weak convergence problems for the implicit iteration process for a finite family of lipschitzian continuous pseudocontractions in general banach spaces the results presented in this paper improve and extend the corresponding ones of xu and ori h k xu r g ori an implicit iteration process for nonexpansive mappings numer funct anal optim 22 2001 767 773 osilike m o osilike implicit iteration process for common fixed points of a finite family of strictly pseudocontractive maps j math anal appl 294 2004 73 81 chen et al r chen y s song h y zhou convergence theorems for implicit iteration process for a finite family of continuous pseudocontractive mappings j math anal appl 314 2006 701 709 and others

the coarse novikov conjecture and banach spaces with property h in this paper we prove the coarse novikov conjecture for metric spaces with bounded geometry which are coarsely embeddable into banach spaces with a geometric condition called property h introduced by g kasparov and g yu

iteration processes for nonlinear lipschitzian strongly accretive mappings in lp spaces abstract suppose x l p or l p 1 p 2 let t x x be a lipschitzian and strongly accretive map with constant k 0 1 and lipschitz constant l satisfying p p 1 l 2 p 2 p 1 1 k define s x x by sx tx x for arbitrary x 0 x the sequence x n n 1 is defined by x n 1 1 n x n n sy n y n 1 n x n n sx n n 0 where n n 1 n n 1 are two real sequences satisfying i 0 n 2 1 p 2 p 1 1 k k n l 2 n p 2 p l 2 1 w n w l 2 1 2 n p 2 p 1 1 k k n l 2 n p 1 2 l 2 1 w n w l 2 1 2 n 1 1 for each n ii 0 n min w w l 2 1 1 w 4 p 1 l 2 k p 1 2 l 2 w 1 for each n iii n n where w p 2 p 1 1 k p 2 p l 2 then x n 1 converges strongly to the unique solution of tx moreover if n 2 1 p 2 p 1 1 k k l 2 p 2 p l 2 1 w w l 2 1 2 p 2 p 1 1 k k l 2 p 1 2 l 2 1 w w l 2 1 2 1 1 and n for each n and some 0 min w w l 2 1 1 w 4 p 1 l 2 k p 1 2 l 2 w 1 then x n 1 q p n 2 x 1 q where q denotes the solution of tx and 1 4 1 p 2 p 1 1 k k l 2 p 2 p l 2 1 w w l 2 1 2 2 p 2 p 1 1 k k l 2 p 1 2 l 2 1 w w l 2 1 2 1 1 0 1 a related result details with the iterative approximation of lipschitz strongly pseudocontractive maps in x

scattering for semilinear wave equations with small data in three space dimensions on considere la theorie de la diffusion pour des equations d onde semilineaires du type u tt u f u a 3 dimensions d espace ou f u u p 1 u ou f u u p r p 1

on hypersphericity of manifolds with finite asymptotic dimension we prove the following embedding theorems in the coarse geometry theorem a every metric space x with bounded geometry whose asymptotic dimension does not exceed n admits a large scale uniform embedding into the product of n 1 locally finite trees corollary every metric space x with bounded geometry whose asymptotic dimension does not exceed n admits a large scale uniform embedding into a non positively curved manifold of dimension 2n 2 the corollary is used in the proof of the following theorem b for every uniformly contractible manifold x whose asymptotic dimension is finite the product x x r is integrally hyperspherical for some n theorem b together with a theorem of gromov lawson implies the result previously proven by g yu 1998 which states that an aspherical manifold whose fundamental group has a finite asymptotic dimension cannot carry a metric of positive scalar curvature we also prove that if a uniformly contractible manifold x of bounded geometry is large scale uniformly embeddable into a hilbert space then x is stably integrally hyperspherical

the coarse geometric novikov conjecture for subspaces of non positively curved manifolds abstract in this paper we prove the coarse geometric novikov conjecture for metric spaces with bounded geometry which admit a coarse embedding into a simply connected complete riemannian manifold of non positive sectional curvature

on picard iterations for strongly accretive and strongly pseudo contractive lipschitz mappings abstract in this note we speed up the convergence of the picard sequence of iterations for strongly accretive and strongly pseudo contractive mappings our results improve the results of chidume c e chidume picard iteration for strongly accretive and strongly pseudo contractive lipschitz maps ictp preprint no ic2000098 c e chidume iterative algorithms for non expansive mappings and some of their generalizations in nonlinear analysis and applications to v lakshmikantham on his 80th birthday vol 1 2 kluwer acad publ dordrecht 2003 pp 383 429 and liu l liu approximation of fixed points of a strictly pseudo contractive mapping proc amer math soc 125 2 1997 1363 1366 and some other known results the technique of the proof presented in this paper is different from the technique used by chidume

an iterative process for nonlinear lipschitzian strongly accretive mappings in lp spaces abstract suppose x l p or l p p 2 let t x x be a lipschitzian and strongly accretive map with constant k 0 1 and lipschitz constant l define s x x by sx f tx x let c n n 1 be a real sequence satisfying 1 i 0 c n k p 1 l 2 2 k 1 1 for each n 2 ii n c n then for arbitrary x 0 x the sequence x n 1 1 c n x n c n sx n n 0 converges strongly to the unique solution of tx f moreover if c n k p 1 l 2 2 k 1 1 for each n then x n 1 q n 2 x 1 q where q denotes the solution of tx f and 1 k p 1 l 2 2 k 1 1 0 1 a related result deals with the iterative approximation of lipschitz strongly pseudocontractive maps in x

the coarse geometric novikov conjecture and uniform convexity abstract the coarse geometric novikov conjecture provides an algorithm to determine when the higher index of an elliptic operator on a noncompact space is nonzero the purpose of this paper is to prove the coarse geometric novikov conjecture for spaces which admit a coarse uniform embedding into a uniformly convex banach space

fixed point solutions of variational inequalities for asymptotically nonexpansive mappings in banach spaces abstract let e be a real banach space with a uniformly g teaux differentiable norm and which possesses uniform normal structure k a nonempty bounded closed convex subset of e t k k an asymptotically nonexpansive mapping with sequence k n n 1 let t n 0 1 be such that t n 1 as n and f be a contraction on k under suitable conditions on the sequence t n we show the existence of a sequence x n n satisfying the relation x n 1 t n k n f x n t n k n t n x n and prove that x n n converges strongly to the fixed point of t which solves some variational inequality provided x n tx n 0 as n as an application we prove that the iterative process defined by z 0 k z n 1 1 t n k n f z n t n k n t n z n n n converges strongly to the same fixed point of t

the equivariant coarse baum connes conjecture for spaces which admit an equivariant coarse embedding into hilbert space abstract in this paper we proved that the equivariant coarse baum connes conjecture holds for a metric space with bounded geometry which admits an equivariant coarse embedding into hilbert space

convergence to common fixed points of averaged mappings without commutativity assumption in hilbert spaces abstract we introduce a new iteration scheme for averaged mappings in hilbert spaces and prove that the iterates converge strongly to common fixed points of the mappings the main theorem extends a recent result of shimizu and takahashi t shimizu w takahashi strong convergence to common fixed points of families of nonexpansive mappings j math anal appl 211 1997 71 83

fibred coarse embedding into non positively curved manifolds and higher index problem abstract let x n 1 x n be the coarse disjoint union of a sequence of finite metric spaces with uniform bounded geometry in this paper we show that the coarse novikov conjecture holds for x if x admits a fibred coarse embedding into a simply connected complete riemannian manifold of non positive sectional curvature this includes a large class of expander graphs with geometric property t

the novikov conjecture for groups with finite asymptotic dimension recall that the asymptotic dimension is a coarse geometric analogue of the covering dimension in topology page 28 14 more precisely the asymptotic dimension for a metric space is the smallest integer n such that for any r 0 there exists a uniformly bounded cover c ui iei of the metric space for which the r multiplicity of c is at most n 1 i e no ball of radius r in the metric space intersects more than n 1 members of c 14 the class of finitely generated discrete groups with finite asymptotic dimension is hereditary in the sense that if a finitely generated group has finite asymptotic dimension as metric space with a word length metric then its finitely generated subgroups also have finite asymptotic dimension as metric spaces with word length metrics cf section 6 this together with a result of gromov in 14 implies that finitely generated subgroups of gromov s hyperbolic groups have finite asymptotic dimension currently no example of a finitely generated group with infinite asymptotic dimension and finite classifying space is known it should also be noted that two different definitions of asymptotic dimension