modeling and vibration control for a flexible pendulum inverted system based on a pde observer abstractthis study addresses the problem of trajectory control of a flexible pendulum inverted system on the basis of the partial differential equation pde and ordinary differential equation ode dynamic model one of the key contributions of this study is that a new model is proposed to simplify the complex system in addition this study proposed a nonlinear pde observer to estimate distributed positions and velocities along flexible pendulum singular perturbation method is proposed to solve the coupling system of nonlinear pde observer the nonlinear pde observer is divided into a fast subsystem and a slow subsystem by the use of the singular perturbation method to stabilise this fast subsystem a boundary controller is proposed at the free end of the beam the sliding mode control method is proposed to design controller for slow subsystems the asymptotic stability of both the proposed nonlinear pde observer and controller is validated by theoretical analysis the results are illustrated by simul

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

hopf algebra of the planar binary trees is a sub hopf algebra there is a basis qn of soln such that the composite map k qn soln k sn has the following property its linear dual k sn k qn is induced by a set theoretic map sn qn in between sn and qn there is an intermediate set yn which is made of planar binary trees with n vertices for instance for n 3 the number of elements in s3 y3 and q3 is 6 5 and 4 respectively the projection from sn to qn is the composite of two maps sn w yn w qn article no ai981759

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

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

control of underactuated spacecraft with bounded inputs bounded feedback control laws are designed for stabilization and tracking of underactuated spacecraft the flat outputs of the system are computed and are used to generate reference trajectories for the tracking problem

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

free algebraic structures on the permutohedra abstract tridendriform algebras are a type of associative algebras introduced independently by f chapoton and by j l loday and the third author in order to describe operads related to the stasheff polytopes the vector space st spanned by the faces of permutohedra has a natural structure of tridendriform bialgebra we prove that it is free as a tridendriform algebra and exhibit a basis our result implies that the subspace of primitive elements of the coalgebra st equipped with the coboundary map of permutohedra is a free cacti algebra

strong convergence of mann s type iterations for nonexpansive semigroups in general banach spaces abstract in this paper we prove a strong convergence theorem of mann s type for commutative nonexpansive semigroups in general banach spaces using this theorem we obtain some strong convergence theorems in general banach spaces

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

synthesized design of a fuzzy logic controller for an underactuated unicycle in this paper we propose synthesized design of a fuzzy logic controller flc for control of an underactuated unicycle system the flc objective is velocity control of the wheel while keeping the pendulum upright which is an unstable equilibrium the synthesized design consists of three phases first the flc structures including the number of rules membership functions inference and parametric relations are chosen based on heuristic knowledge about the unicycle second on the basis of a linearized model and linear feedback the flc output parameters are determined quantitatively for stabilization of the unicycle third the flc output parameters are tuned using an iterative learning tuning ilt algorithm which minimizes an objective function that specifies the desired unicycle performance the rationale for the synthesized flc design is full utilization of the available information which is achieved by combining model based and model free designs and hence improves the flc performance we minimize the number of flc rules and fuzzy labels six rules are used for regulation or setpoint tasks whereas 10 rules are used with extra integral control to eliminate steady state errors induced by system uncertainties and disturbances only two fuzzy labels are adopted for each fuzzy variable the ilt process consists of two phases exploration for stabilization and exploitation for better performance the effectiveness of the proposed flc is validated using intensive simulations and comparisons

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

weak bruhat order on the set of faces of the permutohedron and the associahedron abstract we define a partial order on the set of faces of the permutohedron which extends the weak bruhat order of the symmetric group the restriction of this order gives a partially ordered set structure to the set of faces of the associahedron which extends the tamari order defined on the set of planar binary rooted trees these orders are used to describe associative algebra structures on the vector spaces spanned by the set of faces of the permutohedra on one hand and on the vector space spanned by the set of planar rooted trees on the other hand our results extend the description of the dendriform algebra structure on the spaces spanned by permutations and by planar binary trees in terms of the weak bruhat order and the tamari order respectively obtained by j l loday and the second author in j l loday m ronco order structure and the algebra of permutations and of planar binary trees j algebraic combin 15 2002 253 270

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

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

structure of the malvenuto reutenauer hopf algebra of permutations we analyze the structure of the malvenuto reutenauer hopf algebra ssym of permutations in detail we give explicit formulas for its antipode prove that it is a cofree coalgebra determine its primitive elements and its coradical filtration and show that it decomposes as a crossed product over the hopf algebra of quasi symmetric functions in addition we describe the structure constants of the multiplication as a certain number of facets of the permutahedron as a consequence we obtain a new interpretation of the product of monomial quasi symmetric functions in terms of the facial structure of the cube the hopf algebra of malvenuto and reutenauer has a linear basis indexed by permutations our results are obtained from a combinatorial description of the hopf algebraic structure with respect to a new basis for this algebra related to the original one via mobius inversion on the weak order on the symmetric groups this is in analogy with the relationship between the monomial and funda mental bases of the algebra of quasi symmetric functions our results reveal a close relationship between the structure of the malvenuto reutenauer hopf algebra and the weak order on the symmetric groups

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

the algebra of binary search trees we introduce a monoid structure on the set of binary search trees by a process very similar to the construction of the plactic monoid the robinson schensted insertion being replaced by the binary search tree insertion this leads to a new construction of the algebra of planar binary trees of loday ronco defining it in the same way as non commutative symmetric functions and free symmetric functions we briefly explain how the main known properties of the loday ronco algebra can be described and proved with this combinatorial point of view and then discuss it from a representation theoretical point of view which in turns leads to new combinatorial properties of binary trees

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

time varying exponential stabilization of a rigid spacecraft with two control torques rigid body models with two controls cannot be locally asymptotically stabilized by continuous feedbacks which are functions of the state only this impossibility no longer holds when the feedback is also a function of time and time varying asymptotically stabilizing feedbacks have already been proposed however due to the smoothness of the feedbacks the convergence rate is only polynomial in this paper exponential convergence is obtained by considering time varying feedbacks which are only continuous

sliding mode control of underactuated multibody systems and its application to shape change control in this article we introduce an approach based on sliding mode control to design full state feedback controllers for stabilisation of underactuated non linear multibody systems we define first order sliding surfaces as a linear combination of actuated and unactuated coordinate tracking errors lyapunov stability analysis guarantees that all system trajectories reach and remain on the sliding surfaces however stability of the sliding surfaces depends on the equilibrium manifold if the system has isolated equilibrium points it is linearly controllable and asymptotic stability can be guaranteed under certain conditions otherwise the control system fails brockett s necessary condition for existence of a smooth stabilising feedback in the latter case if the total momentum is conserved the closed loop control system will be marginally stable consequently a procedure is proposed to achieve an asymptotically stable discontinuous control law through sliding surface redefinition and shape changes it i

duality between quasi symmetrical functions and the solomon descent algebra abstract the ring qsym of quasi symmetric functions is naturally the dual of the solomon descent algebra the product and the two coproducts of the first extending those of the symmetric functions correspond to a coproduct and two products of the second which are defined by restriction from the symmetric group algebra a consequence is that qsym is a free commutative algebra

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

controlled lagrangians and the stabilization of mechanical systems i the first matching theorem we develop a method for the stabilization of mechanical systems with symmetry based on the technique of controlled lagrangians the procedure involves making structured modifications to the lagrangian for the uncontrolled system thereby constructing the controlled lagrangian the euler lagrange equations derived from the controlled lagrangian describe the closed loop system where new terms in these equations are identified with control forces since the controlled system is lagrangian by construction energy methods can be used to find control gains that yield closed loop stability we use kinetic shaping to preserve symmetry and only stabilize systems module the symmetry group the procedure is demonstrated for several underactuated balance problems including the stabilization of an inverted planar pendulum on a cart moving on a line and an inverted spherical pendulum on a cart moving in the plane

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

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

algebres de hopf des permutahedres associahedres et hypercubes resume three graded hopf algebras over z are constructed each one having in degree n a basis indexed by the faces of a polytope of dimension n 1 respectively the hypercube the associahedron and the permutahedron this lifts to the level of all faces previous constructions of loday and ronco and malvenuto and reutenauer for vertices of the same polyhedra

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

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

dynamics and control of a class of underactuated mechanical systems this paper presents a theoretical framework for the dynamics and control of underactuated mechanical systems defined as systems with fewer inputs than degrees of freedom control system formulation of underactuated mechanical systems is addressed and a class of underactuated systems characterized by nonintegrable dynamics relations is identified controllability and stabilizability results are derived for this class of underactuated systems examples are included to illustrate the results these examples are of underactuated mechanical systems that are not linearly controllable or smoothly stabilizable

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

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

adaptive variable structure set point control of underactuated robots control of underactuated mechanical systems robots represents an important class of control problem in this correspondence a model based adaptive variable structure control scheme is introduced where the uncertainty bounds only depend on the inertia parameters of the system global asymptotic stability is established in the lyapunov sense numerical simulations are conducted to validate the theoretical analysis

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

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

tridendriform structure on combinatorial hopf algebras we extend the definition of tridendriform bialgebra by introducing a parameter q the subspace of primitive elements of a q tridendriform bialgebra is equipped with an associative product and a natural structure of brace algebra related by a distributive law this data is called q gerstenhaber voronov algebras we prove the equivalence between the categories of conilpotent q tridendriform bialgebras and of q gerstenhaber voronov algebras the space spanned by surjective maps between finite sets as well as the space spanned by parking functions have a natural structure of q tridendriform bialgebra denoted st q and pqsym q in such a way that st q is a sub tridendriform bialgebra of pqsym q finally we show that the bialgebra of m permutations defined by t lam and p pylyavskyy comes from a q tridendriform algebra which is a quotient of st q

fixed points of non expansive mappings associated with invariant means in a banach space in this paper we study the fixed point set of the non expansive mapping t for a banach space with uniformly g teaux differentiable norm when is a multiplicative left invariant mean on l s as an application we establish nonlinear ergodic properties for an extremely amenable semigroup of non expansive mappings in a banach space with uniformly g teaux differentiable norm furthermore we improve a recent result of atsushiba and takahashi s atsushiba w takahashi weak and strong convergence theorems for non expansive semigroups in a banach spaces satisfying opial s condition sci math jpn in press on the fixed point set of non expansive mappings associated with a left invariant mean on a left amenable semigroup

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