weak fixed point property and asymptotic centre for the fourier stieltjes algebra of a locally compact group in this paper we show that the fourier stieltjes algebra b g of a non compact locally compact group g cannot have the weak fixed point property for nonexpansive mappings this answers two open problems posed at a conference in marseille luminy in 1989 we also show that a locally compact group is compact exactly if the asymptotic centre of any non empty weak closed bounded convex subset c in b g with respect to a decreasing net of bounded subsets is a non empty norm compact subset in particular when g is compact b g has the weak fixed point property for left reversible semigroups this generalizes a classical result of t c lim for the circle group as a consequence of our main results we obtain that a number of properties some of which were known to hold for compact groups in fact characterize compact groups

existence of nonexpansive retractions for amenable semigroups of nonexpansive mappings and nonlinear ergodic theorems in banach spaces in this paper we study nonlinear ergodic properties for an amenable semigroup of nonexpansive mappings in a banach space we prove that ifsis an amenable semigroup and s tt t s is a nonexpansive semigroup on a closed convex subsetcin a uniformly convex banach spaceesuch that the setf s of common fixed points of s is nonempty then there exists a nonexpansive retractionpfromcontof s such thatptt ttp pfor eacht sandpx co ttx t s for eachx c in this case there exists a net a of finite averages of s such that for eacht sand for each bounded subsetbofc lim a ttx a x 0 and lim tta x a x 0 uniformly forx b also if the norm ofeis frechet differentiable then for eachx c pxis the unique common fixed point in s s co ttsx t s furthermore if is an asymptotically invariant net of means then for eachx c t x converges weakly topx

nonexpansive retractions in hyperconvex spaces this paper is primarily concerned with the study of conditions on a hyperconvex subset d of a hyperconvex metric space m which assure that there exists a nonexpansive retraction r of m d onto d which has the property that r m d d a related question we take up is when is such a retraction r proximinal that is when does r have the propertydx rx distx dfor each x m among other things we show that if a subset d of a hyperconvex metric space m has nonempty interior and is externally hyperconvex relative to m in a very weak sense then there always exists a nonexpansive retraction of m onto d which maps m d onto d we also show that any compact weakly externally hyperconvex subset of a hyperconvex m is a proximinal nonexpansive retract of m

weak closedness of subspaces of fourier stieltjes algebras and weak continuity of the restriction map let g be a locally compact group and b g the fourier stieltjes algebra of g we study the problem of how weak8 closedness of some translation invariant subspaces of b g is related to the structure of g moreover we prove that for a closed subgroup h of g the restriction map from b g to b h is weak8 continuous only when h is open in g introduction let g be a locally compact group and let b g be the fourier stieltjes algebra of g as defined by eymard 8 recall that b g is the linear span of all continuous positive definite functions on g and can be identified with the banach space dual of c g the group c algebra of g the space b g with the xlorm as dual of c g is a commutative banach algebra with pointwise multiplication and complex conjugation the fourier algebra a g of g is the closed subalgebra of b g generated by the functions in b g with compact support in particular a g is contained in co g the algebra of complex valued continuous functions on g vanishing at infinity as is well known a g is weak dense in b g if and only if g is amenable in 3 translation invariant subalgebras a of b g were studied and it was shown that if such a is weak closed and point separating then it must contain a g however apart from this very little seems to be known about weak closed subspaces of b g the first purpose of this paper is to investigate the relation between weak closedness of certain interesting norm closed translation invariant subspaces of b g and the structure of g secondly we solve the problem of whexl for a closed subgroup h of g the restriction map from b g to b h is weak continuous a brief outline of the paper is as follows in section 2 we estsablish for almost connected locally compact groups g the relation between weclk closed ness of bo g b g n co g in e3 g and the structure of g theorem 2 10 the key result is that for a connected lie group g bo g is weak closed in b g if and only if g is a reductive lie group with compact centre and kazhdan s property t received by the editors december 1s 1995 199l mathematics subject classification primary 22d10 43a30 work supported by nato collaborative research grant crg 940184 g 1997 american mathematical society

nonlinear ergodic theorems of nonexpansive type mappings abstract let s be a semitopological semigroup let c be a closed convex subset of a uniformly convex banach space e whose norm is frechet differentiable and t t t s be a continuous representation of s as almost asymptotically nonexpansive type mapping of c into c such that the common fixed point set f of in c is nonempty in this paper we prove that if s is right reversible then for each x c the closed convex set s s c o t t x t s f consists of at most one point we also prove that if s is reversible then the intersection s s c o t t x t s f is nonempty for each x c if and only if there exists a nonexpansive retraction p of c onto f such that p t t t t p p for all t s and px is in the closed convex hull of t t x t s for each x c

ergodic retractions for amenable semigroups in banach spaces with normal structure abstract in this paper we discuss the existence of nonexpansive retraction onto the set of common fixed points assume that t s s s is an amenable semigroup of nonexpansive mappings on a closed convex subset c in a reflexive banach space e such that the set f of common fixed points of is nonempty among other things it is shown that if either c has normal structure or the t s s are affine then there exists a nonexpansive retraction p from c onto f such that p t t t t p p for each t s and every closed convex invariant subset of c is also p invariant in the case that the mappings are affine p is also affine and p x c o t t x t s for each x c and it is unique regarding the latter property our results extend corresponding results of t suzuki some remarks on the set of common fixed points of one parameter semigroups of nonexpansive mappings in banach spaces with the opial property nonlinear anal 58 2004 441 458 and r e bruck a common fixed point theorem for a commuting family of nonexpansive mappings pacific j math 53 1974 59 71

halin graphs and the travelling salesman problem a halin graphh t c is obtained by embedding a treet having no nodes of degree 2 in the plane and then adding a cyclec to join the leaves oft in such a way that the resulting graph is planar these graphs are edge minimal 3 connected hamiltonian and in general have large numbers of hamilton cycles we show that for arbitrary real edge costs the travelling salesman problem can be polynomially solved for such a graph and we give an explicit linear description of the travelling salesman polytope the convex hull of the incidence vectors of the hamilton cycles for such a graph

fourier stieltjes algebras and measure algebras on compact right topological groups abstract let g be an admissible compact hausdorff right topological group that is a group with a hausdorff topology such that for each a g the map g g a is continuous and the set of a g such that the map g a g is continuous is dense in g such groups arise in the study of distal flows in this paper we study the fourier stieltjes algebra b g the linear span of the continuous positive definite functions on g we show that b g is isomorphic with the fourier stieltjes algebra of an associated compact topological group this result is then applied to obtain some geometric properties including the weak and weak fixed point properties on b g we also study some related properties on the measure algebra m g

a note on approximation of fixed points for amenable semigroups of nonexpansive mappings in banach spaces nonlinear anal 67 2007 1211 1225 abstract in this note we deal with an iterative scheme of halpern type for a semigroup of nonexpansive mappings on a compact convex subset of a strictly convex and smooth banach space with respect to an asymptotically left invariant sequence of means defined on an appropriate space of bounded real valued functions of the semigroup we improve the corresponding result of a t lau h miyake w takahashi approximation of fixed points for amenable semigroups of nonexpansive mappings in banach spaces nonlinear anal 67 2007 1211 1225

fixed point properties of semigroups of non expansive mappings abstract in recent years there have been considerable interests in the study of when a closed convex subset k of a banach space has the fixed point property i e whenever t is a non expansive mapping from k into k then k contains a fixed point for t in this paper we shall study fixed point properties of semigroups of non expansive mappings on weakly compact convex subsets of a banach space or more generally a locally convex space by considering the classes of bicyclic semigroups we answer two open questions one posted earlier by the first author in 1976 dalhousie and the other posted by t mitchell in 1984 virginia we also provide a characterization for the existence of a left invariant mean on the space of weakly almost periodic functions on separable semitopological semigroups in terms of fixed point property for non expansive mappings related to another open problem raised by the first author in 1976

a multi start dynasearch algorithm for the time dependent single machine total weighted tardiness scheduling problem we extend the dynasearch technique recently proposed by congram et al in the context of time dependent combinatorial optimization problems as an application we consider a general time dependent idleness version of the well known single machine total weighted tardiness scheduling problem in which the processing time of a job depends on its starting time of execution we develop a multi start local search algorithm and present experimental results on several types of instances showing the superiority of the dynasearch neighborhood over the traditional one

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

fixed point property for banach algebras associated to locally compact groups abstract in this paper we investigate when various banach algebras associated to a locally compact group g have the weak or weak fixed point property for left reversible semigroups we proved for example that if g is a separable locally compact group with a compact neighborhood of the identity invariant under inner automorphisms then the fourier stieltjes algebra of g has the weak fixed point property for left reversible semigroups if and only if g is compact this generalizes a classical result of t c lim for the case when g is the circle group t

existence of ergodic retractions for semigroups in banach spaces abstract in this work we prove among other results that if s is a right amenable semigroup and t s s s is a quasi nonexpansive semigroup on a closed convex subset c in a strictly convex reflexive banach space e such that the set f of common fixed points of is nonempty then there exists a quasi nonexpansive retraction p from c onto f such that p t t t t p p for each t s and every closed convex invariant subset of c is also p invariant moreover if the mappings are also affine then t g rode an ergodic theorem for semigroups of nonexpansive mappings in a hilbert space j math anal appl 85 1982 172 178 12 is a quasi contractive affine retraction from c onto f such that t t t t t t t for each t s and t x c o t t x t s for each x c and if r is an arbitrary retraction from c onto f such that r x c o t t x t s for each x c then r t it is shown that if the t t s are f quasi contractive then the results hold without the strict convexity condition on e

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

weak fixed point property of reduced fourier stieltjes algebra and generalization of baggett s theorem abstract in this paper we show that if the reduced fourier stieltjes algebra b g of a second countable locally compact group g has either weak fixed point property or asymptotic center property then g is compact as a result we give affirmative answers to open problems raised by fendler and et al in 2013 we then conclude that a second countable group with a discrete reduced dual must be compact this generalizes a theorem of baggett we also construct a compact scattered hausdorff space for which the dual of the scattered c algebra c lacks weak fixed point property the c algebra c provides a negative answer to a question of randrianantoanina in 2010 in addition we prove a variant of bruck s generalized fixed point theorem for the preduals of von neumann algebras furthermore we give some examples emphasizing that the conditions in bruck s generalized conjecture bgc can not be weakened any more

new convexity and fixed point properties in hardy and lebesgue bochner spaces we show that for the hardy class of functions h1 with domain the ball or polydisc in cn a certain type of uniform convexity property the uniform kadec klee huff property holds with respect to the topology of pointwise convergence on the interior which coincides with both the topology of uniform convergence on compacta and the weak topology on bounded subsets of h1 also we show that if a banach space x has a uniform kadec klee huff property then the lebesgue bochner space lp x 1 p must have a related uniform kadec klee huff property consequently by known results the above spaces have normal structure properties and fixed point properties for non expansive mappings

a remark on least squares mixed element methods for reaction diffusion problems in this paper we propose a least squares mixed element procedure for a reaction diffusion problem based on the first order system by selecting the least squares functional properly the resulting procedure can be split into two independent symmetric positive definite schemes one of which is for the unknown variable and the other of which is for the unknown flux variable which lead to the optimal order h 1 w and l 2 w norm error estimates for the primal unknown and optimal h div w norm error estimate for the unknown flux finally we give some numerical examples

nonexpansive retractions and fixed point properties abstract among other results we prove that if a dual banach space e has the weak fixed point property then e has the weak fixed point property for commuting separable semitopological semigroups of nonexpansive mappings and study the existence of ergodic retractions for right amenable semigroups and commuting families of nonexpansive mappings this answers an open problem of lau and mah 1976 12 for commuting separable semi topological semigroups

fixed point set of semigroups of non expansive mappings and amenability abstract in this paper we study the fixed point set of a strongly continuous non expansive semigroup s t t t s of a semi topological semigroup s for which cb s is n extremely left amenable also we study the fixed point set of a strongly continuous semigroup of mappings when s is a semigroup which is a sub semigroup of a locally convex topological vector space with addition some applications to harmonic analysis are also provided

the fixed point property via dual space properties abstract a banach space has the weak fixed point property if its dual space has a weak sequentially compact unit ball and the dual space satisfies the weak uniform kadec klee property and it has the fixed point property if there exists e 0 such that for every infinite subset a of the unit sphere of the dual space a a fails to be 2 e separated in particular e convex banach spaces a class of spaces that includes the uniformly nonsquare spaces have the fixed point property

iterative algorithms for finding common solutions of variational inequalities and systems of equilibrium problems and fixed points of families and semigroups of nonexpansive mappings abstract we introduce iterative algorithms for finding a common element of the set of solutions of a system of equilibrium problems and of the set of fixed points of a finite family and a left amenable semigroup of nonexpansive mappings in a hilbert space we prove the strong convergence of the proposed iterative algorithm to the unique solution of a variational inequality which is the optimality condition for a minimization problem our results extend for example the recent result of v colao g marino h k xu an iterative method for finding common solutions of equilibrium and fixed point problems j math anal appl 344 2008 340 352 to systems of equilibrium problems

the bipartite quadratic assignment problem and extensions abstract we introduce a new binary quadratic program that subsumes the well known quadratic assignment problem this problem is shown to be np hard when some associated parameters are restricted to simple values but solvable in polynomial time when some other parameter values are restricted three different neighborhood structures are introduced a best solution in all these neighborhoods can be identified in polynomial time even though two of these neighborhoods are of exponential size different local search algorithms and their enhancements using tabu search are developed using these neighborhoods experimental analysis show that two hybrid algorithms obtained by combining these neighborhoods in specific ways yield results that are superior to the algorithms that use these neighborhoods separately extensive computational results and statistical analysis of the resulting data are presented

on uniform opial condition and uniform kadec klee property in banach and metric spaces in this paper we define a property that implies uniform opial condition or uniform kadec klee property in banach spaces this will unify many examples in the literature finally we will extend these properties into hyperbolic metric spaces

hybrid pseudo viscosity approximation schemes for systems of equilibrium problems and fixed point problems of infinite family and semigroup of non expansive mappings abstract in this paper we introduce hybrid pseudo viscosity approximation schemes with strongly positive bounded linear operators for finding a common element of the set of solutions to a system of equilibrium problems the set of fixed points of an infinite family and left amenable semigroup of non expansive mappings in the frame work of hilbert spaces our goal is to prove a result of strong convergence for hybrid pseudo viscosity approximation schemes to approach a solution of systems of equilibrium problems which is also a common fixed point of an infinite family and left amenable semigroup of non expansive mappings the results presented in this paper can be treated as an extension and improvement of the corresponding results announced by ceng et al l c ceng q h ansari and j c yao hybrid pseudo viscosity approximation schemes for equilibrium problems and fixed point problems of infinitely many non expansive mappings nonlinear analysis 4 2010 743 754 and many others

a probabilistic analysis of the switching algorithm for the euclidean tsp the well known switching algorithm proposed by lin and kernighan for the euclidean travelling salesman problem has proved to be a simple efficient algorithm for medium size problems though it often gets trapped in local optima although its complexity status is still open it has been observed to be polynomially bounded in practice when applied to uniformly distributed points in the unit square in this paper this polynomial behaviour is derived theoretically however we will come up with a bound of o n18 with probability 1 c n whereas in practice the algorithm works slightly better

polynomially solvable cases of the bipartite traveling salesman problem abstract given two sets r and b consisting of n cities each in the bipartite traveling salesman problem one looks for the shortest way of visiting alternately the cities of r and b returning to the city of origin this problem is known to be np hard for arbitrary sets r and b in this paper we provide an o n 6 algorithm to solve the bipartite traveling salesman problem if the quadrangle property holds in particular this algorithm can be applied to solve in o n 6 time the bipartite traveling salesman problem in the following cases s r b is a convex point set in the plane s r b is the set of vertices of a simple polygon and v r b is the set of vertices of a circular graph for this last case we also describe another algorithm which runs in o n 2 time

a study of exponential neighborhoods for the travelling salesman problem and for the quadratic assignment problem this paper deals with exponential neighborhoods for combinatorial optimization problems exponential neighborhoods are large sets of feasible solutions whose size grows exponentially with the input length we are especially interested in exponential neighborhoods over which the tsp respectively the qap can be solved in polynomial time and we investigate combinatorial and algorithmical questions related to such neighborhoods first we perform a careful study of exponential neighborhoods for the tsp we investigate neighborhoods that can be defined in a simple way via assignments matchings in bipartite graphs partial orders trees and other combinatorial structures we identify several properties of these combinatorial structures that lead to polynomial time optimization algorithms and we also provide variants that slightly violate these properties and lead to np complete optimization problems whereas it is relatively easy to find exponential neighborhoods over which the tsp can be solved in polynomial time the corresponding situation for the qap looks pretty hopeless every exponential neighborhood that is considered in this paper provably leads to an np complete optimization problem for the qap

the weak chebyshev x greedy algorithm in the unweighted bergman space we study a greedy algorithm called the weak chebyshev x greedy algorithm wcxga and investigate its application to unweighted bergman spaces we first show that the wcxga converges for a wide class of real and complex banach spaces and dictionaries we then prove that certain bergman spaces and their holomorphic monomial dictionaries belong to the class of banach spaces for which the wcxga converges

approximation of fixed points for amenable semigroups of nonexpansive mappings in banach spaces abstract the purpose of this paper is to study iterative schemes of browder and halpern types for a semigroup of nonexpansive mappings on a compact convex subset of a smooth and strictly convex banach space with respect to a sequence of strongly asymptotic invariant means defined on an appropriate space of bounded real valued functions of the semigroup various applications to the additive semigroup of nonnegative real numbers and commuting pairs of nonexpansive mappings are also presented

strong convergence for a minimization problem on solutions of systems of equilibrium problems and common fixed points of an infinite family and semigroup of nonexpansive mappings in this paper we introduce a suitable mann type algorithm for finding a common element of the set of solutions of systems of equilibrium problems and the set of common fixed points of an infinite family and left amenable semigroup of nonexpansive mappings in hilbert spaces then we prove the strong convergence of the proposed iterative scheme to the unique solution of the minimization problem on the solution of systems of equilibrium problems and the common fixed points of an infinite family and left amenable semigroup of nonexpansive mappings our results extend and improve the recent result of colao and marino v colao and g marino strong convergence for a minimization problem on points of equilibrium and common fixed points of an infinite family of nonexpansive mappings nonlinear anal 73 2010 3513 3524 and many others

average value of solutions for the bipartite boolean quadratic programs and rounding algorithms we consider domination analysis of approximation algorithms for the bipartite boolean quadratic programming problem bbqp with m n variables a closed form formula is developed to compute the average objective function value a of all solutions in o m n time however computing the median objective function value of the solutions is shown to be np hard also we show that any solution with objective function value no worse than a dominates at least 2 m n 2 solutions and this bound is the best possible further we show that such a solution can be identified in o m n time and hence the domination ratio of this algorithm is at least 1 4 we then show that for any fixed natural numbers a and b such that a b 1 no polynomial time approximation algorithm exists for bbqp with domination ratio larger than 1 2 1 m n unless p np it is shown that some powerful local search algorithms can get trapped at a local maximum with objective function value less than a one of our approximation algorithms has an interesting rounding property which provides a data dependent lower bound on the optimal objective function value a new integer programming formulation of bbqp is also given and computational results with our rounding algorithms are reported

a survey for the quadratic assignment problem the quadratic assignment problem qap one of the most difficult problems in the np hard class models many real life problems in several areas such as facilities location parallel and distributed computing and combinatorial data analysis combinatorial optimization problems such as the traveling salesman problem maximal clique and graph partitioning can be formulated as a qap in this paper we present some of the most important qap formulations and classify them according to their mathematical sources we also present a discussion on the theoretical resources used to define lower bounds for exact and heuristic algorithms we then give a detailed discussion of the progress made in both exact and heuristic solution methods including those formulated according to metaheuristic strategies finally we analyze the contributions brought about by the study of different approaches

a mean ergodic theorem for nonlinear semigroups which are asymptotically nonexpansive in the intermediate sense abstract let x be a uniformly convex banach space such that its dual x has the kadec klee property c a bounded closed convex subset of x and t t t t 0 a one parameter nonlinear semigroup which is asymptotically nonexpansive in the intermediate sense we show that every continuous almost orbit of t is weakly almost convergent to a common fixed point of t a discrete version of our main result is also included

the bilinear assignment problem complexity and polynomially solvable special cases in this paper we study the bilinear assignment problem bap with size parameters m and n m le n bap is a generalization of the well known quadratic assignment problem and the three dimensional assignment problem and hence np hard we show that bap cannot be approximated within a constant factor unless p np even if the associated quadratic cost matrix q is diagonal further we show that bap remains np hard if m o root r of n for some fixed r but is solvable in polynomial time if m o left frac log n log log n right when the rank of q is fixed bap is observed to admit fptas and when this rank is one it is solvable in polynomial time under some additional restrictions we then provide a necessary and sufficient condition for bap to be equivalent to two linear assignment problems a closed form expression to compute the average of the objective function values of all solutions is presented whereas the median of the solution values cannot be identified in polynomial time unless p np we then provide polynomial time heuristic algorithms that find a solution with objective function value no worse than that of m 1 n 1 solutions however computing a solution whose objective function value is no worse than that of m n lceil frac m beta rceil lceil frac n beta rceil solutions is np hard for any fixed rational number beta 1

convergence of a hybrid algorithm for a reversible semigroup of nonlinear operators in banach spaces abstract the purpose of this paper is to study hybrid iterative schemes of halpern types for a semigroup t s s s of relatively nonexpansive mappings on a closed and convex subset c of a banach space with respect to a sequence n of asymptotically left invariant means defined on an appropriate invariant subspace of l s we prove that given a certain sequence n in 0 1 x c we can generate an iterative sequence x n which converges strongly to f x where f x is the generalized projection from c onto the fixed point set f our main result is even new for the case of a hilbert space

characteristic finite element methods for nonlinear sobolev equations1this work is supported by the doctoral fundation of the educational committee of china 1 in this paper the time stepping along characteristic finite element methods for the nonlinear sobolev equation is considered optimal convergence rates in h 1 and l 2 are demonstrated for this scheme numerical results published elsewhere have confirmed that larger time steps are appropriate with these scheme and that the approximations exhibit improved qualitative behavior

construction heuristics for the asymmetric tsp abstract non euclidean traveling salesman problem tsp construction heuristics and especially asymmetric tsp construction heuristics have been neglected in the literature by comparison with the extensive efforts devoted to studying euclidean tsp construction heuristics this state of affairs is at odds with the fact that asymmetric models are relevant to a wider range of applications and indeed are uniformly more general that symmetric models moreover common construction approaches for the euclidean tsp have been shown to produce poor quality solutions for non euclidean instances motivation for remedying this gap in the study of construction approaches is increased by the fact that such methods are a great deal faster than other tsp heuristics which can be important for real time problems requiring continuously updated response the purpose of this paper is to describe two new construction heuristics for the asymmetric tsp and a third heuristic based on combining the other two extensive computational experiments are performed for several different families of tsp instances disclosing that our combined heuristic clearly outperforms well known tsp construction methods and proves significantly more robust in obtaining relatively high quality solutions over a wide range of problems

one local retract and common fixed point for commuting mappings in metric spaces in this paper we introduce and study one local retract of metric spaces in particular we prove that any commutative family of nonexpansive mappings defined on a metric space with a compact and normal convexity structure has a common fixed point this conclusion was known in banach spaces with no similar result in metric spaces

split least squares finite element methods for linear and nonlinear parabolic problems in this paper we propose some least squares finite element procedures for linear and nonlinear parabolic equations based on first order systems by selecting the least squares functional properly each proposed procedure can be split into two independent symmetric positive definite sub procedures one of which is for the primary unknown variable u and the other is for the expanded flux unknown variable s optimal order error estimates are developed finally we give some numerical examples which are in good agreement with the theoretical analysis

a new ilp based refinement heuristic for vehicle routing problems in this paper we address the distance constrained capacitated vehicle routing problem dcvrp where k minimum cost routes through a central depot have to be constructed so as to cover all customers while satisfying for each route both a capacity and a total distance travelled limit

fixed point properties of semigroups of nonexpansive mappings abstract we prove that if h is a hilbert space then the schatten trace class operators on h has the weak fixed point property for left reversible semigroups this answered positively a problem raised by a t m lau we also prove that if m is a finite von neumann algebra then any nonempty bounded convex subset of the non commutative l 1 space associated to m that is compact for the measure topology has the fixed point property for left reversible semigroups

extended neighborhood definition and characterization we consider neighborhood search defined on combinatorial optimization problems suppose that n is a neighborhood for combinatorial optimization problem x we say that n is lo equivalent locally optimal to n if for any instance of x the set of locally optimal solutions with respect to n and n are the same the union of two lo equivalent neighborhoods is itself lo equivalent to the neighborhoods the largest neighborhood that is lo equivalent to n is called the extended neighborhood of n and denoted as n we analyze some basic properties of the extended neighborhood we provide a geometric characterization of the extended neighborhood n when the instances have linear costs defined over a cone for the tsp we consider 2 opt the extended neighborhood for the 2 opt i e 2 exchange neighborhood structure we show that number of neighbors of each tour t in 2 opt is at least n 2 2 we show that finding the best tour in the 2 opt neighborhood is np hard we also show that the extended neighborhood for the graph partition problem is the same as the original neighborhood regardless of the neighborhood defined this result extends to the quadratic assignment problem as well this result on extended neighborhoods relies on a proof that the convex hull of solutions for the graph partition problem has a diameter of 1 that is every two corner points of this polytope are adjacent

sorting jordan sequences in linear time using level linked search trees for a jordan curve c in the plane nowhere tangent to the x axis let x1 x2 xn be the abscissas of the intersection points of c with the x axis listed in the order the points occur on c we call x1 x2 xn a jordan sequence in this paper we describe an o n time algorithm for recognizing and sorting jordan sequences the problem of sorting such sequences arises in computational geometry and computational geography our algorithm is based on a reduction of the recognition and sorting problem to a list splitting problem to solve the list splitting problem we use level linked search trees

strongly amenable semigroups and nonlinear fixed point properties abstract a semi topological semigroup is strongly left amenable if there is a compact left ideal group in the spectrum of its luc compactification in this paper we want to study those objects and study some fixed point property related to non expansive mapping and other similar kind of mapping

some geometric properties on the fourier and fourier stieltjes algebras of locally compact groups arens regularity and related problems let g be a locally compact topological group and a g b g be respectively the fourier and fourier stieltjes algebras of g it is one of the purposes of this paper to investigate the rnp radon nikodym property and some other geometric properties such as weak rnp the dunford pettis property and the schur property on the algebras a g and b g and to relate these properties to the properties of the multiplication operator on the group c algebra c g we also investigate the problem of arens regularity of the projective tensor products c g a when b g c g has the rnp and a is any c algebra some related problems on the measure algebra the group algebra and the algebras a p g pf p g pm p g 1 p are also discussed

first order system least squares for second order partial differential equations part i this paper develops a least squares functional that arises from recasting general second order uniformly elliptic partial differential equations in n 2 or 3 dimensions as a system of first order equations in part i z cai r d lazarov t manteuffel and s mccormick siam j numer anal 31 1994 pp 1785 1799 a similar functional was developed and shown to be elliptic in the h divv times h 1 norm and to yield optimal convergence for finite element subspaces of h divv times h 1 in this paper the functional is modified by adding a compatible constraint and imposing additional boundary conditions on the first order system the resulting functional is proved to be elliptic in the h 1 n 1 norm this immediately implies optimal error estimates for finite element approximation by standard subspaces of h 1 n 1 another direct consequence of this ellipticity is that multiplicative and additive multigrid algorithms applied to the resulting discrete functionals are optimally convergent as an alternative to perturbation based approaches the least squares approach developed here applies directly to convection diffusion reaction equations in a unified way and also admits a fast multigrid solver historically a missing ingredient in least squares methodology

fixed point property and the fourier algebra of a locally compact group we establish some characterizations of the weak fixed point property weak fpp for noncommutative and commutative l 1 spaces and use this for the fourier algebra a g of a locally compact group g in particular we show that if g is an in group then a g has the weak fpp if and only if g is compact we also show that if g is any locally compact group then a g has the fixed point property fpp if and only if g is finite furthermore if a nonzero closed ideal of a g has the fpp then g must be discrete

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

weak convergence and non linear ergodic theorems for reversible semigroups of non lipschitzian mappings abstract letgbe a semitopological semigroup letcbe a closed convex subset of a uniformly convex banach spaceewith afrechetdifferentiable norm and t tt t g be a continuous representation ofgas asymptotically nonexpansive type mappings ofcinto itself such that the common fixed point setf t of t incis nonempty we prove in this paper that ifgis right reversible then for every almost orbitu of t formula consists of at most one point further formula is nonempty for eachx cif and only if there exists a nonexpansive retractionpofcontof t such thatpts tsp pfor alls gandp x is in the closed convex hull of tsx s g x c this result is applied to study the problem of weak convergence of the net u t t g to a common fixed point of t

ritz volterra projections to finite element spaces and applications to integrodifferential and related equations the object of this paper is to investigate the convergence of finite element approximations to solutions of parabolic and hyperbolic integrodifferential equations and also of equations of sobolev and viscoelasticity type the concept of ritz volterra projection will be seen to unify much of the analysis for the different types of problems optimal order error estimates are obtained in l p for 2 leqq p infty and almost optimal order pointwise results given

fixed point properties in hardy spaces abstract we prove that the hardy space h 1 on the unit disc of c has the weak fixed point property for left reversible semigroups

normal structure in dual banach spaces associated with a locally compact group in this paper we investigated when the dual of a certain function space defined on a locally compact group has certain geometric properties more particularly we asked when weak compact convex subsets in these spaces have normal structure and when the norm of these spaces satisfies one of several types of kadec klee property as samples of the results we have obtained we have proved among other things the following two results 1 the measure algebra of a locally compact group has weak normal structure iff it has property sukk iff it has property skk iff the group is discrete 2 among amenable locally compact groups the fourier stieltjes algebra has property sukk iff it has property skk iff the group is compact consequently the fourier stieltjes algebra has weak normal structure when the group is compact

multiobjective traveling salesperson problem on halin graphs in this paper we study traveling salesperson tsp and bottleneck traveling salesperson btsp problems on special graphs called halin graphs although both problems are np hard on general graphs they are polynomially solvable on halin graphs we address the multiobjective versions of these problems we show computational complexities of finding a single nondominated point as well as finding all nondominated points for different objective function combinations we develop algorithms for the polynomially solvable combinations

a remark on split least squares mixed element procedures for pseudo parabolic equations abstract in this paper we introduce two novel split least squares mixed element procedures for pseudo parabolic equations by selecting the least squares functional properly each procedure can be split into two independent symmetric positive definite sub procedures one of sub procedures is for the primitive unknown variable u which is the same as the standard galerkin finite element procedure and the other is for the introduced flux variable optimal order error estimates are developed a numerical example is given to show the efficiency of the introduced schemes

fixed point properties invariant means and invariant projections related to hypergroups abstract let k be a hypergroup with a haar measure this paper consists of two themes fixed point properties for non expansive and affine maps the first theme provides a condition when a non expansive self map on a weak weak compact convex subset of several function spaces over k has a fixed point while the second theme presents some applications of common fixed point properties for affine actions of k

some remarks on the set of common fixed points of one parameter semigroups of nonexpansive mappings in banach spaces with the opial property abstract in this paper we discuss the necessary and sufficient condition for common fixed points of one parameter nonexpansive semigroups in banach spaces with the opial property we next prove the convergence theorem to a common fixed point finally we discuss the existence of nonexpansive retraction onto the set of common fixed points in these theorems we may not assume that the strict uniform convexity of a banach space

the retractions onto the common fixed points of some families and semigroups of mappings abstract assume that c is a closed convex subset of a reflexive banach space e and t i i i is a family of self mappings on c of type such that f the common fixed point set of is nonempty from our results in this paper it can be derived that a if i i f t i is contained in a 3 dimensional subspace of e then f is a nonexpansive retract of c b if is commutative there exists a retraction r of type from c onto f such that r t i t i r r i and every closed convex invariant subset of c is r invariant the same result holds for a non commutative right amenable semigroup under some additional assumptions moreover the existence of a t i ergodic retraction r of type from c x i l e x i c i i onto f in l e for the family is discussed we also apply some of our results to find ergodic retractions for nonexpansive affine mappings