solving boundary value problems for delay differential equations by a fixed point method a general linear boundary value problem for a nonlinear system of delay differential equations dde in short is reduced to a fixed point problem v a v with a properly chosen generally nonlinear operator a the unknown fixed point v is approximated by piecewise linear function v h defined by its values v i v h t i at grid points t i i 0 1 n where n is a given positive integer and h max 1 i n t i t i 1 under suitable assumptions the existence of a fixed point of a is equivalent to existence of so called e h approximate fixed points of v h a v h which can be found by minimization of l 2 n norm of residuum v h a v h with respect to the variables v i these e h approximate fixed points are used for obtaining approximate solutions of the original boundary value problem for a system of dde numerical experiments with the boundary value problem for a system of delay differential equations of population dynamics as well as with two periodic boundary value problems one for the periodic distributed delay lotka volterra competition system and the second one modeling two coupled identical neurons with time delayed connections show an efficiency of this kind of approach

an ergodic theorem for semigroups of nonexpansive mappings in a hilbert space abstract j b baillon c r acad sci paris ser a 280 1975 1511 1514 proved an ergodic theorem for a single nonexpansive mapping in a hilbert space which is a nonlinear version of von neumann s mean ergodic theorem in this paper we study the ergodic behavior of a semigroup of nonexpansive mappings we try to find a sequence of means on the semigroup generalizing the cesaro means on n such that the corresponding sequence of nonexpansive mappings converges to a projection onto the set of common fixed points our method of proof is an appropriate modification of a pazy s proof israel j math 26 1977 197 204 of baillon s theorem

positive periodic solutions of periodic neutral lotka volterra system with state dependent delays by using a fixed point theorem of strict set contraction some new criteria are established for the existence of positive periodic solutions of the following periodic neutral lotka volterra system with state dependent delays dxi t dt xi t ri t j 1naij t xj t j 1nbij t xj t ij t x1 t xn t j 1ncij t xj t ij t x1 t xn t i 1 2 n where ri aij bij cij c r r i j 1 2 n are periodic functions and ij ij c rn 1 r i 1 2 n are periodic functions with respect to their first arguments respectively

strong convergence to common fixed points of families of nonexpansive mappings abstract we introduce iteration schemes for families of nonexpansive mappings in hilbert spaces and prove that the iterates converge strongly to common fixed points of the mappings

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

an abstract existence theorem at resonance and its applications abstract by using brouwer degree theory and a continuation theorem based on mawhin s coincidence degree an abstract existence theorem at resonance for operator equations is developed as applications of this result some sufficient conditions are given for the existence of periodic solutions of semilinear equations at resonance where the kernel of the linear part has dimension n n 2 the results due to nagle and sinkala are generalized improved and unified

periodic solution and almost periodic solution for a nonautonomous lotka volterra dispersal system with infinite delay abstract this paper studies a nonautonomous lotka volterra dispersal systems with infinite time delay which models the diffusion of a single species into n patches by discrete dispersal our results show that the system is uniformly persistent under an appropriate condition the sufficient condition for the global asymptotical stability of the system is also given by using mawhin continuation theorem of coincidence degree we prove that the periodic system has at least one positive periodic solution further obtain the uniqueness and globally asymptotical stability for periodic system by using functional hull theory and directly analyzing the right functional of almost periodic system we show that the almost periodic system has a unique globally asymptotical stable positive almost periodic solution we also show that the delays have very important effects on the dynamic behaviors of the system

periodic solution and global stability for a nonautonomous competitive lotka volterra diffusion system the periodic solution and global stability for a nonautonomous competitive lotka volterra diffusion system is considered in this paper by using of brouwer fixed point theorem and constructing a suitable liapunov function under some appropriate conditions the system has a unique periodic solution which is globally stable

periodic solution for a two species nonautonomous competition lotka volterra patch system with time delay abstract by using the continuation theorem of coincidence degree theory the existence of a positive periodic solution for a two species nonautonomous competition lotka volterra patch system with time delay x 1 t x 1 t r 1 t a 1 t x 1 t b 1 t y t d 1 t x 2 t x 1 t x 2 t x 2 t r 2 t a 2 t x 2 t d 2 t x 1 t x 2 t y t y t r 3 t a 3 t x 1 t b 3 t y t t 0 k s y t s ds is established where ri t ai t i 1 2 3 di t i 1 2 bi t i 1 3 and t are all positive periodic continuous functions with period w 0 is a nonnegative constant and k s is a continuous nonnegative function on 0

nonexpansive retractions and nonlinear ergodic theorems in banach spaces on donne des theoremes ergodiques non lineaires pour des semigroupes commutatifs d applications non dilatation sans utiliser le concept de moyenne compacte

stable periodic solution of a discrete periodic lotka volterra competition system abstract this paper discusses a discrete lotka volterra competition system we first obtain the persistence of the system assuming that the coefficients in the system are periodic we obtain the existence of a periodic solution moreover under some additional conditions this periodic solution is globally stable our results not only reduce to those for the scalar equation when there is no coupling but also improve and complement some in the literature

the weighted universal coxeter group and some related conjectures of lusztig abstract lusztig proposed 15 conjectures for any weighted coxeter groups in this study we explicitly describe kazhdan lusztig cells distinguished involutions and the function a for any weighted universal coxeter group we also verify these conjectures for this group

asymptotic behavior of commutative semigroups of nonexpansive mappings in banachspaces on etablit des theoremes de convergence pour des semigroupes generaux d applications non dilatation dans le cadre des espaces de banach on demontre un theoreme ergodique non lineaire de type rode pour des semigroupes commutatifs

some examples of square integrable representations of semisimple p adic groups we construct irreducible representations of the hecke algebra of an affine weyl group analogous to kilmoyer s reflection representation corresponding to finite weyl groups and we show that in many cases they correspond to a square integrable representation of a simple p adic group

some cells in the weighted coxeter group c n l 2n 1 abstract the fixed point set of the affine weyl group a 2 n 1 s under a certain group automorphism with s s can be considered as the affine weyl group c n s then we study the cells of the weighted coxeter group c n l 2 n 1 with l 2 n 1 the length function of a 2 n 1 we give an explicit description for all the cells of c n l 2 n 1 corresponding to the partitions k 1 2 n 2 k and h 2 n 2 h for any 1 k 2 n 2 and n 1 h 2 n and also for all the cells of c 3 l 7

global stability and asymptotically periodic solution for nonautonomous cooperative lotka volterra diffusion system two asymptotically cooperative lotka volterra populations in the two patch system with diffusion were considered in this paper each population could diffuse independently and discretely between its intrapatch and interpatch by means of constructing a suitable liapunov function we obtained that the systems had a unique asymptotically periodic solution which was globally asymptotically stable