construction of common fixed points of a countable family of λ demicontractive mappings in arbitrary banach spaces we propose iterative mann type schemes to approximate a common fixed point of a countable family of l demicontractive and l lipschitzain mappings this improves the recent result of chidume et al c e chidume m abbas bashir ali convergence of the mann iteration algorithm for a class of pseudocontractive mappings appl math comput 194 1 2007 1 6 from a single strictly pseudocontractive mapping to a family of more general mappings

brauer groups and quotient stacks a natural question is to determine which algebraic stacks are quotient stacks in this paper we give some partial answers and relate it to the question of whether for a scheme x the natural map from the brauer group equivalence classes of azumaya algebras to the cohomological brauer group the torsion subgroup of h 2 x inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i m is surjective

injectivity sets for the radon transform over circles and complete systems of radial functions abstract a necessary and sufficient characterization is given that specifies which sets of sums of translations of radial functions are dense in the set of continuous functions in the plane this problem is shown to be equivalent to inversion for the radon transform on circles centered on restricted subsets of the plane the proofs rest on the geometry of zero sets for harmonic polynomials and the microlocal analysis of this circular radon transform a characterization of nodal sets for the heat and wave equation in the plane are consequences of our theorems and questions of pinkus and ehrenpreis are answered

factorization theorem for projective varieties with finite quotient singularities 1 l is a very ample line bundle and admits two general linearizations l1 and l2 with m l1 m l1 and m l2 m l2 2 the geometric quotient m l1 gln c is isomorphic to x and the geometric quotient m l2 gln c is isomorphic to y 3 the two linearizations l1 and l2 differ only by characters of the c factor and l1 and l2 underly the same linearization of the gln factor let l be this underlying glnlinearization then we have m l m l

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

strong convergence of an implicit iteration process for a finite family of generalized asymptotically quasi nonexpansive maps the aim of this paper is to prove strong convergence of a modified implicit iteration process to a common fixed point for a finite family of generalized asymptotically quasi nonexpansive mappings an immediate corollary of our theorems provides an affirmative response to a question raised by xu and ori h k xu r ori an implicit iterative process for nonexpansive mappings numer funct anal optim 22 2001 767 773

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

coxeter system of lines and planes are sets of injectivity for the twisted spherical means abstract it is well known that a line in r 2 is not a set of injectivity for the spherical means for odd functions about that line we prove that any line passing through the origin is a set of injectivity for the twisted spherical means tsm for functions f l 2 c whose each of spectral projection e 1 4 z 2 f k is a polynomial then we prove that any coxeter system of even number of lines is a set of injectivity for the tsm for l p c 1 p 2 further we deduce that certain coxeter system of even number of planes is a set of injectivity for the tsm for l p c n 1 p 2 we observe that a set s r 2 n 1 c is a set of injectivity for the tsm for a certain class of functions on c n 1

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

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

on mann implicit iterations for strongly accretive and strongly pseudo contractive mappings abstract for a lipschitz strongly accretive map considered by chidume in c e chidume picard iteration for strongly accretive and strongly pseudo contractive lipschitz maps ictp preprint no ic2000098 c e chidume iterative algorithms for nonexpansive mappings and some of their generalizations nonlinear analysis and applications to v lakshmikantam on his 80th birthday vols 1 and 2 kluwer acad publ dordrecht 2003 pp 383 429 it is known that a classical picard type iteration process converges strongly to a zero of the operator he also proved that the rate of convergence in this case is at least as fast as a geometric progression in this paper we study the mann implicit iteration sequence for strongly accretive and strongly pseudo contractive mappings we showed that this implicit scheme gives better convergence rate estimate presented results improve the corresponding results of c e chidume picard iteration for strongly accretive and strongly pseudo contractive lipschitz maps ictp preprint no ic2000098 c e chidume iterative algorithms for nonexpansive mappings and some of their generalizations nonlinear analysis and applications to v lakshmikantam on his 80th birthday vols 1 and 2 kluwer acad publ dordrecht 2003 pp 383 429 l liu approximation of fixed points of a strictly pseudo contractive mapping proc am math soc 125 2 1997 1363 1366 w r sastry g v r babu approximation of fixed points of strictly pseudo contractive mappings on arbitrary closed convex sets in a banach space proc amer math soc 128 2000 2907 2909 y song r chen viscosity approximative methods to cesaro means for non expansive mappings appl math comput 186 2 2007 1120 1128

partial desingularisations of quotients of nonsingular varieties and their betti numbers when a reductive group g acts linearly on a nonsingular complex projective variety x one can define a projective quotient variety x g using mumford s geometric invariant theory if the condition that every semistable point be properly stable is satisfied this quotient is the ordinary topological quotient of an open subset xss of the variety by the group in k a formula is obtained for the rational cohomology of x g under this condition the formula involves the rational cohomology of x and various linear sections of x together with the rational cohomology of the classifying spaces of g and certain reductive subgroups of g in many interesting examples the condition required in k is not satisfied thus the question arises as to what information we can obtain in general the quotient x g can now have serious singularities in contrast to the good case considered in k where the only singularities are those caused by finite isotropy groups it will be shown in this paper that there is a systematic way of blowing up x along a sequence of nonsingular subvarieties to obtain a variety x with a linear action of g such that every semistable point of x is stable the only assumption that we have to make is that there exists at least one stable point of x then x g is almost a resolution of singularities of x1 g in the sense that the most serious singularities have been resolved moreover there is a formula for the rational cohomology of x g again involving the rational cohomology of x and certain linear sections of x together with the rational cohomology of the classifying spaces of g and some reductive subgroups of g see theorem 8 14 for convenience we shall assume throughout that g is connected however the construction of x works in general and it is straightforward to modify the cohomological formulas to apply to the general case the construction of x g can also be modified to apply in some cases when x has no stable points the layout of the paper is as follows section 1 is a review of the basic facts of geometric invariant theory which will be needed and section 2 describes the relationship of geometric invariant theory with symplectic geometry and the moment map in section 3 semistability and stability in a blow up of x along a nonsingular c invariant subvariety are related to semistability and stability in x

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

on mann iteration in hilbert spaces abstract let k be a compact convex subset of a real hilbert space h t k k a hemicontractive map let n be a real sequence in 0 1 satisfying appropriate conditions then for arbitrary x 0 k the sequence x n defined iteratively by x n n x n 1 1 n t x n n 1 converges strongly to a fixed point of t

zeros and mapping theorems for perturbations of m accretive operators in banach spaces let x be a real banach space and t d t x 2 x be an m accretive operator let c d t x x be a bounded operator not necessarily continuous such that c t i 1 is compact suppose that for every x d t with x r there exists jx jx such that 0 for all u tx then we have 0 t c d t b r 0 where b r 0 denotes the open ball of x with centre at zero and radius r 0 assume furthermore that t d t 2 x is strongly accretive then 0 t c d t b r 0 as applications of the above zero theorem we derive many new mapping theorems for perturbations of m accretive operators in banach spaces when t and c are odd operators we also obtain some new mapping theorems

injectivity sets for spherical means on the heisenberg group in this paper we prove that cylinders of the form r s r r where s r is the sphere z c n z r are injectivity sets for the spherical mean value operator on the heisenberg group h n in l p spaces we prove this result as a consequence of a uniqueness theorem for the heat equation associated to the sub laplacian a hecke bochner type identity for the weyl transform proved by d geller and spherical harmonic expansions are the main tools used

iterative methods for the computation of fixed points of demicontractive mappings this paper surveys some of the main convergence properties of the mann type iteration for the demicontractive mappings some variants of the mann iteration that ensure the strong convergence like the cq algorithm and a variant for the asymptotically demicontractive mappings are also considered the usual framework of our study is a real hilbert space and only to a certain extent some particular banach spaces historical aspects are pointed out and some applications for the convex feasibility problem are discussed

convergence of the mann iteration algorithm for a class of pseudocontractive mappings let k be a nonempty closed and convex subset of a real banach space e let t k k be a strictly pseudocontractive map in the sense of browder and petryshyn for a fixed x email protected k define a sequence x n byx n 1 email protected n x email protected ntx n where a n is a real sequence defined in 0 1 satisfying the following conditions i n 1 email protected n ii n 1 email protected n 2 email protected x n tx email protected 0 if in addition t is demicompact then x n converges strongly to some fixed point of t

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

viscosity approximative methods to cesaro means for non expansive mappings abstract in this paper we defined viscosity iterative sequence zm and xn of the cesaro means for non expansive mappings t and proved that zm and xn converge strongly to some p f t respectively where p is a unique solution in f t to the following variational inequality f i p j u p 0 for all u f t our results developed and complemented the corresponding ones by shin ya matsushita and daishi kuroiwa strong convergence of averaging iterations of nonexpansive nonself mappings j math anal appl 294 2004 206 214 and h k xu viscosity approximation methods for nonexpansive mappings j math anal appl 298 2004 279 291 and yongfu su and suhong li strong convergence theorems on two iterative method for non expansive mappings appl math comput available from accessed 28 02 06

revisiting hardy s theorem for the heisenberg group we establish several versions of hardy s theorem for the fourier transform on the heisenberg group let hat f lambda be the fourier transform of a function f on h n and assume hat f lambda ast hat f lambda leq c hat p 2b lambda where p s is the heat kernel associated to the sublaplacian we show that if f z t leq c p a z t then f 0 whenever a b there are infinitely many linearly independent functions f satisfying both conditions on f lambda and hat f lambda

a note on the paper a new iteration process for generalized lipschitz pseudo contractive and generalized lipschitz accretive mappings abstract in this note we will modify several gaps in chidume and ofoedu c e chidume e u ofoedu a new iteration process for generalized lipschitz pseudo contractive and generalized lipschitz accretive mappings nonlinear anal 2006 in press doi 10 1016 j na 2006 05 012

spherical means wave equations and hermite laguerre expansions abstract in this paper we study the maximal function associated to the weyl transformw r of the normalised surface measure ron the sphere z rin c n this operator is given by the expansion w r f k 0 k n 1 k n 1 phiv k r p k f where kare laguerre functions of type n 1 andpkare hermite projection operators we show that whenp 2n 2n 1 the maximal operator supr 0 w r f x is bounded onlp r n using this we study almost everywhere convergence to initial data of solutions of the wave equation associated to the hermite operator the above expansion forw r motivates the study of operators of the form s t f k 0 phiv k t p k f wherephiv kare laguerre functions of type we study various mapping properties of these operators with applications to hermite expansions and solutions of darboux type equations

a note on the error estimation of the mann iteration in this note a new formula of error estimation of the mann iteration and a sufficient condition of strong convergence of strongly demicontractive mappings are obtained moreover some numerical examples are also given our results improve and extend the corresponding results in a recent article l maruster and st maruster 2015

iterative solution of nonlinear equations of the φ strongly accretive type abstract letq 1 and letebe a realq uniformly smooth banach space lett e ebe a lipschitz strongly accretive operator and suppose the equationtx f f e has a solution it is proved that under suitable conditions on the real sequences n n 0 and n n 0 the iteration process formula converges strongly to the unique solution of the equationtx f a related result deals with the approximation of fixed points of hemicontractive operators a class of operators which is much more general than the important class of strongly pseudocontractive operators

toroidal varieties and the weak factorization theorem we develop the theory of stratified toroidal varieties which gives together with the theory of birational cobordisms 73 a proof of the weak factorization conjecture for birational maps in characteristic zero a birational map between complete nonsingular varieties over an algebraically closed field k of characteristic zero is a composite of blow ups and blow downs with smooth centers

modified noor iterations for nonlinear equations in banach spaces the purpose of this paper is to analyze the modified three step iterative scheme for solving nonlinear operator equations in real banach spaces our results can be viewed as an extension of three step and two step iterative schemes of glowinski and le tallec r glowinski p le tallec augemented lagrangian and operator splitting methods in nonlinear mechanics siam publishing co philadelphia 1989 noor m a noor three step iterative algorithms for multivalued quasi variational inclusions j math anal appl 255 2001 589 604 m a noor some predictor corrector algorithms for multivalued variational inequalities j optim theory appl 108 3 2001 659 670 m a noor t m rassias z huang three step iterations for nonlinear accretive operator equations j math anal appl 274 2002 59 68 and ishikawa s ishikawa fixed points by a new iteration method proc amer math soc 44 1974 147 150

on the error estimation and t stability of the mann iteration abstract a formula of error estimation of mann iteration is given in the case of strongly demicontractive mappings based on this estimation a condition of strong convergence is obtained for the same class of mappings t stability for a particular case of strongly demicontractive mappings is proved some numerical examples showing the accuracy of the proposed estimations are also given

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

iterative approximations of fixed points and solutions for strongly accretive and strongly pseudo contractive mappings in banach spaces abstract in this article we prove some new convergence theorems of the ishikawa and mann iteration sequences for strongly accretive and strongly pseudo contractive mappings by using the new inequality and the new approximation methods our main results improve and extend the corresponding results of j math anal appl 151 1990 453 461 proc amer math soc 120 1994 545 551 j math appl 192 1995 502 518 j math anal appl 174 1993 441 449 acta appl math 32 1993 183 196 nonlinear anal tma 24 1995 981 987 j math anal appl 178 1993 9 21 proc amer math soc 125 6 1997 1705 1709