on the convergence of hybrid projection algorithms for asymptotically quasi φ nonexpansive mappings using the mann iteration in an infinite dimensional hilbert space only weak convergence theorems are obtained even for nonexpansive mappings the purpose of this paper is to modify the mann iteration and prove the strong convergence theorems without any compactness assumption for asymptotically quasi f nonexpansive mappings moreover strong convergence theorems are also established in a uniformly smooth and strictly convex banach space with the kadec klee property

strong convergence theorems by hybrid methods for families of nonexpansive mappings in hilbert spaces abstract in this paper we prove a strong convergence theorem by the hybrid method for a family of nonexpansive mappings which generalizes nakajo and takahashi s theorems k nakajo w takahashi strong convergence theorems for nonexpansive mappings and nonexpansive semigroups j math anal appl 279 2003 372 379 simultaneously furthermore we obtain another strong convergence theorem for the family of nonexpansive mappings by a hybrid method which is different from nakajo and takahashi using this theorem we get some new results for a single nonexpansive mapping or a family of nonexpansive mappings in a hilbert space

asymptotic equivalence of neutral and infinite retarded differential equations staffan a demontre qu une equation differentielle fonctionnelle fde neutre avec d operateur stable peut souvent etre traitee comme une fde a retard avec retardement infini le but principal de l article est d illustrer comment les techniques de staffans peuvent etre employees pour etudier le comportement asymptotique de solutions de certaines fde neutres non lineaires et non autonomes en particulier on considere une equation neutre scalaire de la forme d dt x t cx t r f t x t x t r

asymptotic constancy for pseudo monotone dynamical systems on function spaces abstract a pseudo monotone dynamical system is a dynamical system which preserves the order relation between initial points and equilibrium points the purpose of this paper is to present some convergence oscillation and order stability criteria for pseudo monotone dynamical systems on function spaces for which each constant function is an equilibrium point some applications to neutral functional differential equations and semilinear parabolic partial differential equations with neumann boundary condition are given

strong convergence theorems for monotone mappings and relatively weak nonexpansive mappings in this paper we prove strong convergence theorems to a zero of monotone mapping and a fixed point of relatively weak nonexpansive mapping moreover strong convergence theorems to a point which is a fixed point of relatively weak nonexpansive mapping and a solution of a certain variational problem are proved under appropriate conditions

flots et series de taylor stochastiques we study the expansion of the solution of a stochastic differential equation as an infinite sum of iterated stochastic stratonovitch integrals this enables us to give a universal and explicit formula for any invariant diffusion on a lie group in terms of lie brackets as well as a universal and explicit formula for the brownian motion on a riemannian manifold in terms of derivatives of the curvature tensor the first of these formulae contains and extends to the non nilpotent case the results of doss 6 sussmann 17 yamato 18 fliess and normand cyrot 7 krener and lobry 19 and kunita 11 on the representation of solutions of stochastic differential equations

ornstein uhlenbeck processes with singular drifts integral estimates and girsanov densities we consider a perturbation of a hilbert space valued ornstein uhlenbeck process by a class of singular nonlinear non autonomous maximal monotone time dependent drifts the only further assumption on the drift is that it is bounded on balls in the hilbert space uniformly in time first we introduce a new notion of generalized solutions for such equations which we call pseudo weak solutions and prove that they always exist and obtain pathwise estimates in terms of the data of the equation then we prove that their laws are absolutely continuous with respect to the law of the original ornstein uhlenbeck process in particular we show that pseudo weak solutions always have continuous sample paths in addition we obtain integrability estimates of the associated girsanov densities some of our results concern non random equations as well while probabilistic results are new even in finite dimensional autonomous settings

on a hybrid method for a family of relatively nonexpansive mappings in a banach space we prove strong convergence theorems by the hybrid method given by takahashi takeuchi and kubota for a family of relatively nonexpansive mappings under weaker conditions the method of the proof is different from the original one and it shows that the type of projection used in the iterative method is independent of the properties of the mappings we also deal with the problem of finding a zero of a maximal monotone operator and obtain a strong convergence theorem using this method

weak and strong convergence theorems for strict pseudo contractions in hilbert spaces abstract let c be a closed convex subset of a real hilbert space h and assume that t is a strict pseudo contraction on c with a fixed point for some 0 1 given an initial guess x 0 c and given also a real sequence n in 0 1 the mann s algorithm generates a sequence x n by the formula x n 1 n x n 1 n t x n n 0 it is proved that if the control sequence n is chosen so that n 1 and n 0 n 1 n then x n converges weakly to a fixed point of t however this convergence is in general not strong we then modify mann s algorithm by applying projections onto suitably constructed closed convex sets to get an algorithm which generates a strong convergent sequence this result extends a recent result of nakajo and takahashi k nakajo w takahashi strong convergence theorems for nonexpansive mappings and nonexpansive semigroups j math anal appl 279 2003 372 379 from nonexpansive mappings to strict pseudo contractions

strong convergence theorems based on a new modified extragradient method for variational inequality problems and fixed point problems in banach spaces in this paper we introduce a new iterative algorithm by a modified extragradient method for finding a common element of the set of solutions of a general variational inequality and the set of common fixed points of an infinite family of k i strict pseudocontractions in a banach space we obtain some strong convergence theorems under suitable conditions the results obtained in this paper improve and extend the recent ones announced by many others

asymptotic equivalence of differential equations and asymptotically almost periodic solutions abstract in this paper we use rab s lemma m rab uber lineare perturbationen eines systems von linearen differentialgleichungen czechoslovak math j 83 1958 222 229 m rab note sur les formules asymptotiques pour les solutions d un systeme d equations differentielles lineaires czechoslovak math j 91 1966 127 129 to obtain new sufficient conditions for the asymptotic equivalence of linear and quasilinear systems of ordinary differential equations yakubovich s result v v nemytskii v v stepanov qualitative theory of differential equations princeton university press princeton new jersey 1966 v a yakubovich on the asymptotic behavior of systems of differential equations mat sb 28 1951 217 240 on the asymptotic equivalence of a linear and a quasilinear system is developed on the basis of the equivalence the existence of asymptotically almost periodic solutions of the systems is investigated the definitions of biasymptotic equivalence for the equations and biasymptotically almost periodic solutions are introduced theorems on the sufficient conditions for the systems to be biasymptotically equivalent and for the existence of biasymptotically almost periodic solutions are obtained appropriate examples are constructed

asymptotic behavior of solutions for a class of difference equations abstract consider the difference equation x n x n 1 f x n g x n k eqno 1 wherekis a positive integer fandgare continuous andfis increasing onr we show that whenf y g y fory r every solution of 1 tends to either a constant or asn while whenf y g y fory r every solution of 1 tends to either a constant or asn in particular iff y g y fory r then every solution of 1 tends to a constant asn

bounded oscillation criteria for certain third order nonlinear difference equations with several delays and advances this paper deals with the third order nonlinear difference equations with several delays and advances d a email protected 2x n f n x n x n d 1 n x n d k n 0 n n 0 and d a email protected 2x n b ng x n x n d 1 n x n d k n 0 n n 0 sufficient conditions of the existence of uncountably many bounded positive negative and nonoscillatory solutions respectively and necessary and sufficient conditions of the bounded oscillation of and with certain asymptotic behavior are given in addition a sufficient condition of the oscillatory behavior of all bounded solutions of with a special of asymptotic property is also presented nine nontrivial examples which dwell upon the importance of the results obtained in this paper are also included

the campbell baker hausdorff dynkin formula and solutions of differential equations the campbell baker hausdorff dynkin formula is a special case of a simpler and more general formula for the solution of nonautonomous systems of first order ordinary differential equations in terms of autonomous systems specifically suppose u t takes values in a c manifold and satisfies the initial value problem u t a t u t u 0 a where a t is a vector field on the manifold depending continuously on t then u t exp z t a here exp z a means the solution at s 1 to v s z v s v 0 a for z t r 1 pr e r2r 1e tr t x a s 1 a s 2 a s r ds as t 0 where tr t s rr 0 s1 s2 sr t pr is the set of permutations on 1 r e is the number of errors in ordering consecutive terms in 1 r and is the usual commutator of vector fields under appropriate analyticity assumptions the series for z t is convergent for small t this formula gives an explicit formulation of results of k t chen published in 1957 applications are given to problems in sub riemannian geometry and to improving convergence estimates for the campbell baker hausdorff dynkin formula in the context of banach algebras our formula can be thought of as a noncommutative generalization of the familiar formula u t a exp 0t a s ds in the scalar linear case in the same way that the campbell baker hausdorff dynkin formula is a noncommutative generalization of the familiar formula exey ex y

convergence of solutions for a class of neutral difference equations abstract consider the neutral difference equation x n cx n k f n x n x n k where k is a positive integer 0 c y n y n y n 1 f n r 2 r is continuous and decreasing with respect to the second argument we give the results that solutions of the equation convergent to constants

on hybrid projection methods for asymptotically quasi φ nonexpansive mappings the purpose of this paper is to consider the problem of approximating a common fixed point of two asymptotically quasi f nonexpansive mappings based on hybrid projection methods strong convergence theorems are established in a real banach space

heat kernel analysis on semi infinite lie groups this paper studies brownian motion and heat kernel measure on a class of infinite dimensional lie groups we prove a cameron martin type quasi invariance theorem for the heat kernel measure and give estimates on the lp norms of the radon nikodym derivatives we also prove that a logarithmic sobolev inequality holds in this setting

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

logarithmic sobolev inequalities for pinned loop groups abstract letgbe a connected compact type lie group equipped with anadg invariant inner product on the lie algebra g ofg given this data there is a well known left invariant h1 riemannian structure on l l g the infinite dimensional group of continuous based loops ing using this riemannian structure we define and construct a heat kernel t g0 associated to the laplace beltrami operator on l g heret 0 g0 l g and t g0 is a certain probability measure on l g for fixedg0 l g andt 0 we use the measure t g0 and the riemannian structure on l g to construct a classical pre dirichlet form the main theorem of this paper asserts that this pre dirichlet form admits a logarithmic sobolev inequality

a subelliptic taylor isomorphism on infinite dimensional heisenberg groups let g denote an infinite dimensional heisenberg like group which is a class of infinite dimensional step 2 stratified lie groups we consider holomorphic functions on g that are square integrable with respect to a heat kernel measure which is formally subelliptic in the sense that all appropriate finite dimensional projections are smooth measures we prove a unitary equivalence between a subclass of these square integrable holomorphic functions and a certain completion of the universal enveloping algebra of the cameron martin lie subalgebra the isomorphism defining the equivalence is given as a composition of restriction and taylor maps

a neutral fde with stable d operator is retarded abstract a neutral functional differential equation with a linear autonomous and stable d operator can be rewritten as a retarded functional differential equation with infinite delay this fact can be used e g in the study of the stability of the neutral equation and to simplify the proofs of some standard asymptotic results

convergence theorems and asymptotic integration for functional differential equations abstract this paper is devoted to the investigation on convergence of solutions and asymptotic integration of some functional differential equations fdes in the first part of the paper some convergence criteria are obtained and an invariance principle is established for the convergence of solutions of linear fdes under perturbations and disturbances with l 1 integrable coefficients these theorems are applicable to some nonlinear or nonhomogeneous equations in the second part the convergence theorems are applied to investigate the asymptotic integration of some linear fdes this research is made mainly to discuss a situation that was avoided by some previous literature some examples are given to illustrate the theorems

square integrable holomorphic functions on infinite dimensional heisenberg type groups we introduce a class of non commutative complex infinite dimensional heisenberg like lie groups based on an abstract wiener space the holomorphic functions which are also square integrable with respect to a heat kernel measure on these groups are studied in particular we establish a unitary equivalence between the square integrable holomorphic functions and a certain completion of the universal enveloping algebra of the lie algebra of this class of groups using quasi invariance of the heat kernel measure we also construct a skeleton map which characterizes globally defined functions from the l 2 closure of holomorphic polynomials by their values on the cameron martin subgroup

asymptotic behavior of solutions for a class of nonlinear difference equations abstract in this paper we study the asymptotic behavior of solutions for a class of nonlinear difference equations and give the results about the solutions of the equations convergent to a constant our results generalize all conclusions obtained in 1

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 theorems for relatively nonexpansive mappings in a banach space abstract in this paper we prove two strong convergence theorems of modified ishikawa iteration and modified halpern iteration for relatively nonexpansive mappings in a banach space our results extend and improve the recent ones announced by nakajo takahashi kim martinez yanes xu and some others

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

integration by parts and quasi invariance for heat kernel measures on loop groups abstract integration by parts formulas are established both for wiener measure on the path space of a loop group and for the heat kernel measures on the loop group the wiener measure is defined to be the law of a certain loop group valued brownian motion and the heat kernel measures are time t t 0 distributions of this brownian motion a corollary of either of these integrations by parts formulas is the closability of the pre dirichlet form considered by b k driver and t lohrenz 1996 j functional anal 140 381 448 we also show that the heat kernel measures are quasi invariant under right under right and left translations by finite energy loops

asymptotic expansion of stochastic flows we study the asymptotic expansion in small time of the solution of a stochastic differential equation we obtain a universal and explicit formula in terms of lie brackets and iterated stochastic stratonovich integrals this formula contains the results of doss 6 sussmann 15 fliess and normand cyrot 7 krener and lobry 10 yamato 17 and kunita 11 in the nilpotent case and extends to general diffusions the representation given by ben arous 3 for invariant diffusions on a lie group the main tool is an asymptotic expansion for deterministic ordinary differential equations given by strichartz 14

quasi invariance of brownian measures on the group of circle homeomorphisms and infinite dimensional riemannian geometry abstract a cameron martin type theorem is proved for the canonical brownian motion on the group of homeomorphisms of the circle

heat kernel analysis on infinite dimensional heisenberg groups abstract we introduce a class of non commutative heisenberg like infinite dimensional lie groups based on an abstract wiener space the ricci curvature tensor for these groups is computed and shown to be bounded brownian motion and the corresponding heat kernel measures t t 0 are also studied we show that these heat kernel measures admit 1 gaussian like upper bounds 2 cameron martin type quasi invariance results 3 good l p bounds on the corresponding radon nikodym derivatives 4 integration by parts formulas and 5 logarithmic sobolev inequalities the last three results heavily rely on the boundedness of the ricci tensor

strong convergence of modified mann iterations for asymptotically nonexpansive mappings and semigroups abstract the mann iterations for nonexpansive mappings have in general only weak convergence in a hilbert space we modify an iterative method of mann s type introduced by nakajo and takahashi strong convergence theorems for nonexpansive mappings and nonexpansive semigroups j math anal appl 279 2003 372 379 for nonexpansive mappings and prove strong convergence of our modified mann s iteration processes for asymptotically nonexpansive mappings and semigroups

asymptotic behavior of linear impulsive integro differential equations asymptotic equilibria of linear integro differential equations and asymptotic relations between solutions of linear homogeneous impulsive differential equations and those of linear integro differential equations are established a new gronwall bellman type lemma for integro differential inequalities is proved an example is given to demonstrate the validity of one of the results

on some algorithms in banach spaces finding fixed points of nonlinear mappings abstract by using a modification of the hybrid method in mathematical programming we give some new algorithm to find out a fixed point of mappings which are in some sense non expansive our results hold in reflexive strictly convex smooth banach spaces with the kadec klee property