caristi s fixed point theorem and selections of set valued contractions we show without the axiom of choice that the zermelo theorem implies directly a restriction of the caristi fixed point theorem to continuous functions under the axiom of choice this restriction is proved to be equivalent to caristi s theorem we also discuss kirk s problem on an extension of the caristi theorem and we establish two selection theorems for set valued contractions

fixed points of asymptotic contractions abstract let r r be a contractive gauge function in the sense that is continuous s 0 and if f m m satisfies d f x f y d x y for all x y in a complete metric space m d then f always has a unique fixed point it is proved that if t m m satisfies d t n x t n y n d x y x y m where each n is continuous and n uniformly on the range of d then t has a unique fixed point and moreover all of the picard iterates of t converge to this fixed point

pointwise lipschitzian mappings in uniformly convex and uniformly smooth banach spaces abstract let x be a uniformly convex and uniformly smooth banach space let t c c be an asymptotic pointwise nonexpansive mapping where c is a bounded closed and convex subset of x in this paper we investigate conditions sufficient for the weak convergence of the generalized mann and ishikawa processes to a fixed point of t

best proximity points for asymptotic cyclic contraction mappings abstract in this paper we prove the existence and convergence of best proximity points for asymptotic cyclic contractions in metric spaces with the property uc as well as for asymptotic proximal pointwise contractions in uniformly convex banach spaces moreover we consider a generalized cyclic contraction mapping and prove the existence of best proximity points for such a mapping in banach spaces which do not necessarily satisfy the geometric property uc

function variational principles and coercivity abstract the function type extension of ekeland s variational principle j math anal appl 47 1974 324 353 due to zhong nonlinear anal 29 1997 1421 1431 is deductible in a simplified manner and in a larger functional context this is also true for his normed coercivity result based on palais smale techniques

fixed point theorems for φ k i j mappings abstract we introduce a new notion of gauge function and establish a general fixed point theorem for the new class of not necessary contractive the k i j mappings the convergence speed of the iterative sequence f n x to the fixed point in this theorem is at least exponential but f n x does not satisfy in general any inequality of the form d f n x f n 1 x d f n 1 x f n x with 1 moreover we can have d f n x f n 1 x d f n 1 x f n x for infinitely many integers n the theorem is given in the more general setting of quasi metric spaces special cases of which are the metric spaces some special theorems are also given

multifractal analysis of conformal axiom a flows we develop the multifractal analysis of conformal axiom a flows this includes the study of the hausdorff dimension of basic sets of the flow the description of the dimension spectra for pointwise dimension and for lyapunov exponents and the multifractal decomposition associated with these spectra the main tool of study is the thermodynamic formalism for hyperbolic flows by bowen and ruelle examples include suspensions over axiom a conformal diffeomorphisms anosov flows and in particular geodesic flows on compact smooth surfaces of negative curvature

a rate of convergence for asymptotic contractions abstract in p gerhardy a quantitative version of kirk s fixed point theorem for asymptotic contractions j math anal appl 316 2006 339 345 p gerhardy gives a quantitative version of kirk s fixed point theorem for asymptotic contractions this involves modifying the definition of an asymptotic contraction subsuming the old definition under the new one and giving a bound expressed in the relevant moduli and a bound on the picard iteration sequence on how far one must go in the iteration sequence to at least once get close to the fixed point however since the convergence to the fixed point needs not be monotone this theorem does not provide a full rate of convergence we here give an explicit rate of convergence for the iteration sequence expressed in the relevant moduli and a bound on the sequence we furthermore give a characterization of asymptotic contractions on bounded complete metric spaces showing that they are exactly the mappings for which every picard iteration sequence converges to the same point with a rate of convergence which is uniform in the starting point

generalized caristi s fixed point theorems by bae and others abstract in this paper we extend the generalized caristi s fixed point theorems proved by bae j math anal appl 284 2003 690 697 and others

scattering theory and the trace of the wave group in 9 lax and phillips discuss the analogue for classical scattering theories in odd space dimensions of the poisson summation formula as generalized to compact manifolds by chazarain 3 colin de verdi e 141 and duistermaat and guillemin 5 and further generalized to manifolds with boundary in 1 71 however in 9 this trace formula is only proved for comparatively large values of the time variable see also ralston 14 1 bardos el al 2 this note is devoted to the proof of the same formula for all positive time for the case of scattering by a smooth compactly supported potential if n a is the number of poles a 3 then for every e 0 there exists c 0 such that

fixed point theorems in boolean vector spaces in this paper we obtain some fixed and common fixed point theorems in finite dimensional normed boolean vector spaces our results extend and unify some known results

complex scaling and the distribution of scattering poles the purpose of this paper is to establish sharp polynomial bounds on the number of scattering poles for a general class of compactly supported self adjoint perturbations of the laplacian in r n odd we also consider more general types of bounds that give sharper estimates in certain situations the general conclusion can be stated as follows the order of growth of the poles is the same as the order of growth of eigenvalues for corresponding compact problems from the few known cases however the exact asymptotics are expected to be different the scattering poles for compactly supported perturbations were rigorously defined by lax and phillips 13 in a more general setting they correspond to resonances the study of which has a long tradition in mathematical physics in the lax phillips theory they appear as the poles of the meromorphic continuation of the scattering matrix and coincide with the poles of the meromorphic continuation of the resolvent of the perturbed operator because of the latter characterization they can be considered as the analogue of the discrete spectral data for problems on noncompact domains the problem of estimating the counting function

geometric bounds on the density of resonances for semiclassical problems in this paper we shall give upper bounds on the number of resonances in certain regions in the complex plane close to the real axis for semiclassical operators like h 2 v x when h is small

extensions and applications of acf mappings abstract using a definition of asf sequences derived from the definition of asymptotic contractions of the final type of acf we give some new fixed point theorem for cyclic mappings and an alternating mapping which extend results from suzuki 2007 8 theorem 2 and zhang 2007 10 theorem 1

generalized contractions of meir keeler type endpoints set valued dynamical systems and generalized pseudometrics in uniform spaces abstract this paper gives the concepts of w families of generalized pseudodistances families of generalized gauge maps and set valued dynamical systems of w contractions of meir keeler type in hausdorff complete uniform spaces and a method which is useful for establishing conditions guaranteeing the existence and uniqueness of endpoints of these contractions and the convergence to these endpoints of all generalized sequences of iterations of these contractions the definitions the results and the method presented here are new for set valued dynamical systems in uniform locally convex and metric spaces and even for single valued maps the paper includes examples which show a fundamental difference between our results and the well known ones

quantum decay rates in chaotic scattering we study quantum scattering on manifolds equivalent to the euclidean space near infinity in the semiclassical regime we assume that the corresponding classical flow admits a non trivial trapped set and that the dynamics on this set is of axiom a type uniformly hyperbolic we are interested in the distribution of quantum resonances near the real axis in two dimensions we prove that if the trapped set is sufficiently thin then there exists a gap between the resonances and the real axis that is quantum decay rates are bounded from below in higher dimension the condition for this gap is given in terms of a certain topological pressure associated with the classical flow under the same assumption we also prove a resolvent estimate with a logarithmic loss compared to non trapping situations

comultiplication for shifted yangians and quantum open toda lattice abstract we study a coproduct in type a quantum open toda lattice in terms of a coproduct in the shifted yangian of sl 2 at the classical level this corresponds to the multiplication of scattering matrices of euclidean s u 2 monopoles we also study coproducts for shifted yangians for any simply laced lie algebra

fixed point theorem for asymptotic contractions of meir keeler type in complete metric spaces abstract in this paper we introduce the notion of asymptotic contraction of meir keeler type and prove a fixed point theorem for such contractions which is a generalization of fixed point theorems of meir keeler and kirk in our discussion we use the characterization of meir keeler contraction proved by lim on characterizations of meir keeler contractive maps nonlinear anal 46 2001 113 120 we also give a simple proof of this characterization

lower bounds on the number of scattering poles ii abstract we obtain lower bounds on the number of scattering poles for a class of abstract compactly supported perturbations of the laplacian in r n n odd they are applied to estimate the number of resonances for obstacle scattering and for hypoelliptic compactly supported perturbations of the laplacian the proof involves a development of lax phillips theory in a generalized setting a poisson formula for scattering poles and some simple tauberian arguments

on some nonlinear problems induced by an abstract maximal element principle abstract in this paper by applying an abstract maximal element principle on quasi ordered sets established by lin and du we obtain a generalized brezis browder principle system vectorial versions of ekeland s variational principle and maximal element principle and a vectorial version of takahashi s nonconvex minimization theorem moreover we investigate the equivalence between scalar versions and vectorial versions of these results

best proximity points for cyclic meir keeler contractions abstract we introduce a notion of cyclic meir keeler contractions and prove a theorem which assures the existence and uniqueness of a best proximity point for cyclic meir keeler contractions this theorem is a generalization of a recent result due to eldred and veeramani

ekeland s variational principle minimax theorems and existence of nonconvex equilibria in complete metric spaces abstract in this paper we introduce the concept of function which generalizes the concept of w distance studied in the literature we establish a generalized ekeland s variational principle in the setting of lower semicontinuous from above and functions as applications of our ekeland s variational principle we derive generalized caristi s common fixed point theorems a generalized takahashi s nonconvex minimization theorem a nonconvex minimax theorem a nonconvex equilibrium theorem and a generalized flower petal theorem for lower semicontinuous from above functions or lower semicontinuous functions in the complete metric spaces we also prove that these theorems also imply our ekeland s variational principle

common fixed points of almost generalized contractive mappings in ordered metric spaces the existence theorems of common fixed points for two weakly increasing mappings satisfying an almost generalized contractive condition in ordered metric spaces are proved some comparative example are constructed which illustrate the values of the obtained results in comparison to some of the existing ones in literature

fixed point results for a generalized nonexpansive map in uniformly convex metric spaces abstract in this paper the existence of a unique fixed point of a map satisfying a very general contractive condition on a suitable subset of a uniformly convex metric space is proved this fixed point is approximated by averaging krasnosel skii iterations of a generalized nonexpansive map our results substantially improve and extend several known results existing in the literature

quasi asymptotic contractions set valued dynamic systems uniqueness of endpoints and generalized pseudodistances in uniform spaces abstract for set valued dynamic systems in uniform spaces we introduce the concept of quasi asymptotic contractions with respect to some generalized pseudodistances describe a method which we use to establish general conditions guaranteeing the existence and uniqueness of endpoints stationary points of these contractions and exhibit conditions such that for each starting point each generalized sequence of iterations in particular each dynamic process converges and the limit is an endpoint the definition result ideas and techniques are new for set valued dynamic systems in uniform locally convex and metric spaces and even for single valued maps

asymptotic pointwise contractions a simple and elementary without using the ultrapower technique proof for the existence of a fixed point of an asymptotic pointwise contraction is provided the existence of fixed points for asymptotic pointwise nonexpansive mappings in a uniformly convex banach space is also investigated

contractions of banach tarafdar meir keeler ciric jachymski matkowski and suzuki types and fixed points in uniform spaces with generalized pseudodistances in the uniform spaces sequentially complete and not sequentially complete we introduce the concept of the j families of generalized pseudodistances we apply it to construct j generalized contractions and we provide the conditions guaranteeing the existence and uniqueness of fixed points of these contractions and the convergence to these fixed points of each iterative sequence of these contractions our j generalized contractions essentially extend banach tarafdar meir keeler ciric jachymski matkowski and suzuki contractions to uniform spaces with j families of generalized pseudodistances examples showing a difference between our results and the well known ones are given the definitions the results and the method to investigate uniqueness and iterative approximation of fixed points of the maps presented here are new for maps in uniform and locally convex spaces and even in metric spaces

remarks on a paper by f browder about contraction throughout this note x denotes a complete metric space with distance function d and t is a map from x into itself powers of t are defined by tax x and t lx t t x n 2 0 occasionally we use the notation xk tkx in particular x0 x x1 tx for the sake of brevity the set x tx t x t x is called an orbit starting at x and denoted by o x the set 0 x y is the union of the two orbits starting at x and y 0 x y xk yk k 3 o the diameter diam a of a nonempty subset a of x is the supremum of the numbers d x y where x and y vary in a the letter 4 denotes a contractive gauge function i e a continuous increasing function from r the non negative reals into r which satisfies 4 s 0

three fixed point theorems for generalized contractions with constants in complete metric spaces abstract we prove three fixed point theorems for generalized contractions with constants in complete metric spaces which are generalizations of very recent fixed point theorems due to suzuki we also raise one problem concerning the constants

a fixed point theorem for weakly zamfirescu mappings abstract in 5 zamfirescu 1972 gave a fixed point theorem that generalizes the classical fixed point theorems by banach kannan and chatterjea in this paper we follow the ideas of dugundji and granas to extend zamfirescu s fixed point theorem to the class of weakly zamfirescu maps a continuation method for this class of maps is also given

a definitive result on asymptotic contractions abstract we generalize a fixed point theorem for asymptotic contractions due to kirk w a kirk fixed points of asymptotic contractions j math anal appl 277 2003 645 650 our result is the final generalization in some sense

cone uniform cone locally convex and cone metric spaces endpoints set valued dynamic systems and quasi asymptotic contractions abstract the concepts of cone pseudometrics cone uniform spaces generated by these pseudometrics cone pseudodistances set valued quasi asymptotic contractions with respect to these pseudodistances and cone closed maps are introduced and studied conditions guaranteeing the existence and uniqueness of endpoints stationary points of these contractions and conditions ensuring that for each starting point each generalized sequence of iterations of these contractions in particular each dynamic process converges and then the limit is an endpoint are all established also the concept of the cone locally convex space as a special case of the cone uniform space is introduced and examples of quasi asymptotic contractions in cone metric spaces are constructed the definitions results ideas and methods are new for set valued dynamic systems in cone uniform cone locally convex and cone metric spaces and even for single valued maps in these spaces

contractivity of leader type and fixed points in uniform spaces with generalized pseudodistances abstract recently jachymski and jo wik proved that among various classes of contractions which are introduced and studied in the metric fixed point theory the leader contractions are greatest general contractions in this article we want to show how generalized pseudodistances in uniform spaces can be used to obtain new and general results of leader type without complete graph assumptions about maps and without sequentially complete assumptions about spaces which was not done in the previous publications on this subject the definitions results and methods presented here are new for maps in uniform and locally convex spaces and even in metric spaces examples showing a difference between our results and the well known ones are given

the uniqueness of endpoints for set valued dynamical systems of contractions of meir keeler type in uniform spaces abstract in this paper the concept of the set valued dynamical systems of contractions of meir keeler type in uniform spaces is introduced and conditions guaranteeing the existence and uniqueness of endpoints of these contractions and the convergence to these endpoints of all generalized sequences of iterations of these contractions are established the definition and the result presented here are new for set valued dynamical systems in uniform locally convex and metric spaces and even for single valued maps examples show a fundamental difference between our result and the well known ones

mann iteration process for asymptotic pointwise nonexpansive mappings in metric spaces abstract let m d be a complete 2 uniformly convex metric space let c be a nonempty bounded closed and convex subset of m and let t c c be an asymptotic pointwise nonexpansive mapping in this paper we prove that the modified mann iteration process defined by x n 1 t n t n x n 1 t n x n converges in a weaker sense to a fixed point of t

on the relation between the weak palais smale condition and coercivity given by zhong abstract in this paper we discuss zhong s result that the weak palais smale condition implies coercivity under some assumption given in c k zhong a generalization of ekeland s variational principle and application to the study of the relation between the weak p s condition and coercivity nonlinear anal 29 1997 1421 1431 we also give a simple proof of zhong s result further we generalize the result of caklovic li and willem l caklovic s j li m willem a note on palais smale condition and coercivity differential integral equations 3 1990 799 800

on maximal element theorems variants of ekeland s variational principle and their applications abstract in this paper we establish several different versions of generalized ekeland s variational principle and maximal element theorem for functions in complete metric spaces the equivalence relations between maximal element theorems generalized ekeland s variational principle generalized caristi s common fixed point theorems and nonconvex maximal element theorems for maps are also proved moreover we obtain some applications to a nonconvex minimax theorem nonconvex vectorial equilibrium theorems and convergence theorems in complete metric spaces

neumann resonances in linear elasticity for an arbitrary body we study resonances scattering poles associated to the elasticity operator in the exterior of an arbitrary obstacle inr3 with neumann boundary conditions we prove that there exists a sequence of resonances tending rapidly to the real axis

viscosity solutions of hamilton jacobi equations with unbounded nonlinear terms abstract the aim of this paper is to introduce a new definition of viscosity solutions for hamilton jacobi equations in infinite dimensions with unbounded nonlinear terms we prove existence and uniqueness results under usual assumptions regarding the bounded part of the hamiltonian

approximating fixed points of a pair of contractive type mappings in generalized convex metric spaces in this paper we consider an ishikawa type iteration process with errors which converges to the unique common fixed point of a pair of contractive type mappings in complete generalized convex metric spaces furthermore we obtain the corresponding results in banach spaces our results extend and generalize many known results

on a fixed point theorem of kirk abstract w a kirk j math anal appl 277 2003 645 650 first introduced the notion of asymptotic contractions and proved the fixed point theorem for this class of mappings in this note we present a new short and simple proof of kirk s theorem

new fixed point theorems for asymptotically regular multi valued maps abstract recently extending ciric s quasi contraction to a very general setting proinov petko d proinov fixed point theorems in metric spaces nonlinear anal 64 2006 546 557 obtained a remarkable fixed point theorem we utilize proinov s contractive type hypotheses for a self map of a metric space to obtain very general fixed point theorems for multi valued maps in metric spaces

bethe subalgebras in yangians and the wonderful compactification let mathfrak g be a complex simple lie algebra we study the family of bethe subalgebras in the yangian y mathfrak g parameterized by the corresponding adjoint lie group g we describe their classical limits as subalgebras in the algebra of polynomial functions on the formal lie group g 1 t 1 in particular we show that for regular values of the parameter these subalgebras are free polynomial algebras with the same poincare series as the cartan subalgebra of the yangian next we extend the family of bethe subalgebras to the de concini procesi wonderful compactification overline g supset g and describe the subalgebras corresponding to generic points of any stratum in overline g as bethe subalgebras in the yangian of the corresponding levi subalgebra in mathfrak g in particular we describe explicitly all bethe subalgebras corresponding to the closure of the maximal torus in the wonderful compactification

on asymptotic pointwise contractions in metric spaces abstract we discuss the existence of fixed points of asymptotic pointwise mappings in metric spaces this is the nonlinear version of some known results proved in banach spaces we also discuss the case of multivalued mappings

on characterizations of meir keeler contractive maps let x d be a metric space a map t x x is called meir keeler contractive if 0 0 such that d x y d tx ty we introduce l functions and characterize meir keeler contractive maps as maps that satisfy d tx ty d x y for some l function this characterization makes it easy to compare such maps with those satisfying the boyd wong s condition

a generalization of the banach contraction principle with high order of convergence of successive approximations in this paper we present the following generalization of the banach contraction principle let t d x xt d x x be a continuous operator on a complete metric space x d x d satisfying d tx t2x d x tx for all x d tx d with d x tx j where j r j r is an interval containing 0 j j j j is a gauge function of order r 1r 1 on jj in the sense that 0 0 t tr 0 0 t tr is nondecreasing on j 0 j 0 and t t t t on j 0 j 0 suppose that x0 dx0 d is an initial point such that d x0 tx0 jd x0 tx0 j and all of the iterates xn 1 txn n 0 1 belong to dd then the iterative sequence xn 1 txnxn 1 txn converges to a fixed point of tt with error estimates d xn sn r 1 rnd x0 tx0 andd xn d xn xn 1 1 d xn xn 1 where sn r 1 r rn 1 d x0 tx0 sn r 1 r rn 1 d x0 tx0 and is a nonnegative and nondecreasing function on jj such that t t t this fixed point theorem includes as special cases some results of mysovskih i p mysovskih on the convergence of l v kantorovic s method of solution of functional equations and its applications dokl acad nauk sssr 70 1950 565 568 in russian rheinboldt w c rheinboldt a unified convergence theory for a class of iterative processes siam j numer anal 5 1968 42 63 gel man a gel man a certain fixed point principle dokl akad nauk sssr 198 1971 506 508 in russian soviet math dokl 12 1971 813 816 engl transl huang z d huang on newton s method under holder continuous derivative j math anal appl 270 2002 332 339 and others

the strong ekeland variational principle abstract in this paper we consider the strong ekeland variational principle due to georgiev p g georgiev the strong ekeland variational principle the strong drop theorem and applications j math anal appl 131 1988 1 21 we discuss it for functions defined on banach spaces and on compact metric spaces we also prove the distance version of it

approximation of common fixed points of weakly compatible pairs using the jungck iteration abstract we show that the jungck iteration scheme can be used to approximate the common fixed points of some weakly compatible pairs of generalized quasicontractive operators defined on metric spaces the existence of coincidence points are also discussed for those pair of maps the results are generalizations of well known results of the convergence of picard iterations for single self maps of banach spaces in particular the results improve generalize and extend the recent results of berinde v berinde a common fixed point theorem for compatible quasi contractive self mappings in metric spaces applied mathematics and computation 213 2009 348 354 and answers the open question posed in the paper

existence and uniqueness of endpoints of closed set valued asymptotic contractions in metric spaces abstract investigations of problems of set valued asymptotic fixed point theory of set valued dynamic systems are initiated the concepts of the set valued asymptotic contractions of set valued dynamic systems t m 2 m in metric space m are introduced and conditions guaranteeing the existence and uniqueness of endpoints v m of set valued dynamic systems of set valued asymptotic contractions t m 2 m and convergence to v of all generalized sequences of iterations of t are established examples and remarks show a fundamental difference between our results and the well known ones

two generalizations of some fixed point theorems the aim of this paper is to generalize two classical fixed point theorems given by bogin j bogin a generalization of a fixed point theorem of goebel kirk and shimi canad math bull 19 1976 7 12 and gregus m gregus a fixed point theorem in banach spaces boll un math ital a 5 17 1980 193 198 we also complement and extend some very recent results proved by suzuki t suzuki a generalized banach contraction principle that characterizes metric completeness proc amer math soc 136 2008 1861 1869

on asymptotic pointwise nonexpansive mappings in modular function spaces we prove the existence of fixed points of asymptotic pointwise nonexpansive mappings in modular function spaces

generalized distance and existence theorems in complete metric spaces abstract in this paper we first introduce the concept of distance on a metric space which is a generalized concept of both w distance and tataru s distance we also improve the generalizations of the banach contraction principle caristi s fixed point theorem ekeland s variational principle and the nonconvex minimization theorem according to takahashi further we discuss the relation between w distance and tataru s distance

fixed point theorems in metric spaces abstract in this paper we establish two general theorems for equivalence between the meir keeler type contractive conditions and the contractive definitions involving gauge functions one of these theorems is an extension of a recent result of lim on characterization of meir keeler contractive maps nonlinear anal 46 2001 113 120 also we establish the following new fixed point theorem suppose r r is a contractive gauge function in the sense that for any e 0 there exists e such that e t implies t e and suppose t is a continuous and asymptotically regular selfmapping on a complete metric space x d satisfying the following i d tx ty d x y for all x y x and ii d tx ty d x y for all x y x with x y where d x y d x y d x tx d y ty with 0 then t has a unique fixed point and all of the picard iterates of t converge to this fixed point this result includes those of jachimski equivalent conditions and the meir keeler type theorems j math anal appl 194 1995 293 303 matkowski fixed point theorems for contractive mappings in metric spaces cas pest mat 105 1980 341 344 and others

a new type of fixed point theorem in metric spaces abstract we prove a generalization of edelstein s fixed point theorem though there are thousands of fixed point theorems in metric spaces our theorem is a new type of theorem

a generalized distance and enhanced ekeland s variational principle for vector functions we propose a definition of lower closed transitive relations and prove the existence of minimal elements for such a relation this result is shown to contain probably a large part of existing versions of ekeland s variational principle evp we introduce the notion of a weak function p as a generalized distance and use it together with the above result on minimal elements to establish enhanced evp for various settings under relaxed lower semicontinuity assumptions these principles conclude the existence not only of p strict minimizers of p perturbations of the considered vector function but also p sharp and p strong minimizers our results are proved to be stronger than the classical evp and many generalizations in the literature even in the usual one dimensional case by numerous corollaries and examples we include equivalent formulations of our enhanced evp as well

characterizations of reflexivity and compactness via the strong ekeland variational principle it is well known that the famous ekeland variational principle characterizes the metric completeness of underlying spaces in this paper we prove that some versions of the strong ekeland variational principle characterize the reflexivity and the compactness of underlying spaces

feigin frenkel center in types b c and d for each simple lie algebra mathfrak g consider the corresponding affine vertex algebra v mathrm crit mathfrak g at the critical level the center of this vertex algebra is a commutative associative algebra whose structure was described by a remarkable theorem of feigin and frenkel about two decades ago however only recently simple formulas for the generators of the center were found for the lie algebras of type a following talalaev s discovery of explicit higher gaudin hamiltonians we give explicit formulas for generators of the centers of the affine vertex algebras v mathrm crit mathfrak g associated with the simple lie algebras mathfrak g of types b c and d the construction relies on the schur weyl duality involving the brauer algebra and the generators are expressed as weighted traces over tensor spaces and equivalently as traces over the spaces of singular vectors for the action of the lie algebra mathfrak sl 2 in the context of howe duality this leads to explicit constructions of commutative subalgebras of the universal enveloping algebras mathrm u mathfrak g t and mathrm u mathfrak g and to higher order hamiltonians in the gaudin model associated with each lie algebra mathfrak g we also introduce analogues of the bethe subalgebras of the yangians mathrm y mathfrak g and show that their graded images coincide with the respective commutative subalgebras of mathrm u mathfrak g t

an extension of lakzian rhoades results in the structure of ordered b metric spaces via wt distance with an application abstract in this present article we establish two new kinds of nonlinear contraction mappings to obtain fixed point results in the structure of ordered b metric space via wt distance in fact our presented results are extensions of recent theorems due to lakzian rhoades 2019 appl math comput and other existing classical results of fixed point theory furthermore we provide examples to show the validity of our new investigations as an application we apply our new findings to obtain solution of a matrix equation finally we verify the accuracy of our new results numerically

bethe subalgebras in twisted yangians we study analogues of the yangian of the lie algebra mathfrak g mathfrak l n for the other classical lie algebras mathfrak s mathfrak o n and mathfrak s mathfrak p n we call them twisted yangians they are coideal subalgebras in the yangian of mathfrak g mathfrak l n and admit homomorphisms onto the universal enveloping algebras u mathfrak s mathfrak o n and u mathfrak s mathfrak p n respectively in every twisted yangian we construct a family of maximal commutative subalgebras parametrized by the regular semisimple elements of the corresponding classical lie algebra the images in u mathfrak s mathfrak o n and u mathfrak s mathfrak p n of these subalgebras are also maximal commutative

some generalizations of ekeland type variational principle with applications to equilibrium problems and fixed point theory abstract in this paper we introduce the concept of a q function defined on a quasi metric space which generalizes the notion of a function and a w distance we establish ekeland type variational principles in the setting of quasi metric spaces with a q function we also present an equilibrium version of the ekeland type variational principle in the setting of quasi metric spaces with a q function we prove some equivalences of our variational principles with caristi kirk type fixed point theorems for multivalued maps the takahashi minimization theorem and some other related results as applications of our results we derive existence results for solutions of equilibrium problems and fixed point theorems for multivalued maps we also extend the nadler s fixed point theorem for multivalued maps to a q function and in the setting of complete quasi metric spaces as a consequence we prove the banach contraction theorem for a q function and in the setting of complete quasi metric spaces the results of this paper extend and generalize many results appearing recently in the literature

endpoints of set valued dynamical systems of asymptotic contractions of meir keeler type and strict contractions in uniform spaces abstract in this paper we introduce the concepts of the set valued dynamical systems of asymptotic contractions of meir keeler type and set valued dynamical systems of strict contractions in uniform spaces and we present a method which is useful for establishing conditions guaranteeing the existence and uniqueness of endpoints of these contractions and the convergence to these endpoints of all generalized sequences of iterations of these contractions the result concerning the investigations of problems of the set valued asymptotic fixed point theory include some well known results of meir and keeler kirk and suzuki concerning the asymptotic fixed point theory of single valued maps in metric spaces the result concerning set valued strict contractions in which the contractive coefficient is not constant is different from the result of yuan concerning the existence of endpoints of tarafdar vyborny generalized contractions in which the contractive coefficient is constant in bounded metric spaces and provides some examples of tarafdar yuan topological contractions in compact uniform spaces definitions and results presented here are new for set valued dynamical systems in uniform locally convex and metric spaces and even for single valued maps examples show a fundamental difference between our results and the well known ones

the selberg zeta function for convex co compact schottky groups we give a new upper bound on the selberg zeta function for a convex co compact schottky group acting on the hyperbolic space n 1 in strips parallel to the imaginary axis the zeta function is bounded by exp c s where is the dimension of the limit set of the group this bound is more precise than the optimal global bound exp c s n 1 and it gives new bounds on the number of resonances scattering poles of n 1 the proof of this result is based on the application of holomorphic l2 techniques to the study of the determinants of the ruelle transfer operators and on the quasi self similarity of limit sets we also study this problem numerically and provide evidence that the bound may be optimal our motivation comes from molecular dynamics and we consider n 1 as the simplest model of quantum chaotic scattering

on a class of representations of the yangian and moduli space of monopoles a new class of infinite dimensional representations of the yangians yopen image in new window and yopen image in new window corresponding to a complex semisimple algebra open image in new window and its borel subalgebra open image in new window is constructed it is based on the generalization of the drinfeld realization of open image in new window in terms of quantum minors to the case of an arbitrary semisimple lie algebra open image in new window the poisson geometry associated with the constructed representations is described in particular it is shown that the underlying symplectic leaves are isomorphic to the moduli spaces of g monopoles defined as the components of the space of based maps of 1 into the generalized flag manifold open image in new window thus the constructed representations of the yangian may be considered as a quantization of the moduli space of the monopoles

a quantitative version of kirk s fixed point theorem for asymptotic contractions abstract in w a kirk fixed points of asymptotic contractions j math anal appl 277 2003 645 650 w a kirk introduced the notion of asymptotic contractions and proved a fixed point theorem for such mappings using techniques from proof mining we develop a variant of the notion of asymptotic contractions and prove a quantitative version of the corresponding fixed point theorem

subrahmanyam s fixed point theorem abstract we give a sufficient and necessary condition for the convergence of the sequence of successive approximations to a fixed point which is the conclusion of subrahmanyam s fixed point theorem

a note on a paper of i d arandelovic on asymptotic contractions abstract w a kirk w a kirk fixed points of asymptotic contractions j math anal appl 277 2003 645 650 defined the notion of an asymptotic contraction on a metric space and using ultrapower techniques he gave a nonconstructive proof of an asymptotic version of the boyd wong fixed point theorem subsequently i d arandelovic i d arandelovic on a fixed point theorem of kirk j math anal appl 301 2005 384 385 established somewhat more general version of kirk s result and he gave an elementary proof of it however our purpose is to show that there is an error in this proof and moreover arandelovic s theorem is false we also explain how to correct this result

on kirk s asymptotic contractions abstract recently kirk introduced the notion of asymptotic contractions on a metric space and using ultrapower techniques he obtained an asymptotic version of the boyd wong fixed point theorem in this paper we extend this result and moreover we give a constructive proof of it furthermore we obtain a complete characterization of asymptotic contractions on a compact metric space as a by product we establish a separation theorem for upper semicontinuous functions satisfying some limit condition