h asymptotic stability by fixed point in neutral nonlinear differential equations with delay abstract we use fixed point theory to obtain h asymptotic stability results about the zero solution of nonlinear differential equations with functional delay neither boundedness of the deviations nor a fixed sign on the coefficients functions are asked an explicit estimation of the solutions is obtained and a necessary and sufficient condition is determined classical results are improved and generalized

fixed points and stability of neutral stochastic delay differential equations in this paper we consider a linear scalar neutral stochastic differential equation with variable delays and give conditions to ensure that the zero solution is asymptotically mean square stable by means of fixed point theory these conditions do not require the boundedness of delays nor do they ask for a fixed sign on the coefficient functions an asymptotic mean square stability theorem with a necessary and sufficient condition is proved some well known results are improved and generalized

the stability of neutral stochastic delay differential equations with poisson jumps by fixed points in the paper the asymptotic mean square stability of the zero solution for neutral stochastic delay differential equations with poisson jumps is studied by fixed points theory without lyapunov functions the coefficient functions have not been asked for a fixed sign and the sufficient condition for mean square stability has been obtained therefore some well known results are improved and generalized

the distribution function inequality and products of toeplitz operators and hankel operators abstract in this paper we study hankel operators and toeplitz operators through a distribution function inequality on the lusin area integral function and the littlewood paley theory a sufficient condition and a necessary condition are obtained for the boundedness of the product of two hankel operators they lead to a way to approach sarason s conjecture on products of toeplitz operators and shed light on the compactness of the product of hankel operators an elementary necessary and sufficient condition for the product of two toeplitz operators to be a compact perturbation of a toeplitz operator is obtained moreover a necessary condition is given for the product of hankel operators to be in the commutator ideal of the algebra generated by the toeplitz operators with symbols in a sarason algebra

every completely polynomially bounded operator is similar to a contraction it is proved that a bounded operator on a hilbert space is similar to a contraction if and only if it is completely polynomially bounded this gives a partial answer to problem 6 of halmos bull amer math soc 76 1970 877 933 the set of completely bounded maps between c algebras is studied to obtain some structure representation and extension theorems for this class of maps these allow a characterization of the completely bounded representations on a hilbert space of any subalgebra of a c algebra to be obtained the result in the title follows by applying this characterization to the disk algebra

fixed points and stability in linear neutral differential equations with variable delays in this paper we consider the asymptotic stability of a generalized linear neutral differential equation with variable delays by using the fixed point theory an asymptotic stability theorem with a necessary and sufficient condition is proved which improves and generalizes some results due to burton 2003 3 zhang 2005 14 raffoul 2004 13 and jin and luo 2008 12 two examples are also given to illustrate our results

study the stability of solutions of functional differential equations via fixed points in this paper we study the stability properties of solutions of a class of functional differential equations with variable delay by using the fixed point theory under an exponentially weighted metric we obtain some interesting sufficient conditions ensuring that the zero solution of the equations is stable and asymptotically stable

study of the stability in nonlinear neutral differential equations with functional delay using krasnoselskii burton s fixed point in this paper we use a modification of krasnoselskii s fixed point theorem introduced by burton 2002 see 6 theorem 3 to obtain stability results of the zero solution of the totally nonlinear neutral differential equations with functional delayx email protected ddtqt email protected gt xt email protected stability of the zero solution of this equation provided that h0 qt 0 gt 0 0 0 the caratheodory condition is used for the functions q and g

unitary colligations reproducing kernel hilbert spaces and nevanlinna pick interpolation in several variables abstract recently j agler studied the class s d of scalar valued analytic functions of d complex variables f for which f t 1 t d has norm at most 1 for any collection of d commuting contractions t 1 t d on a hilbert space h among other results he obtained a characterization of such functions in terms of a positivity property and in terms of a representation as the transfer function of a certain type of d variable linear system as well as a nevanlinna pick interpolation theorem for this class of functions in this note we examine the system theory aspects and uniqueness of the transfer function representation and give a simpler proof of the nevanlinna pick interpolation theorem for the class s d and obtain a d variable version of the toeplitz corona theorem by using ideas of arov and grossman introduced for 1 variable problems as a bonus we obtain a collection of linear fractional maps which parametrize the set of all s d solutions of an interpolation problem

on the stability of a second order retarded differential equation in this paper we study a second order retarded differential equation with variable delay applying the fixed point theory we obtain a necessary and sufficient condition ensuring that the zero solution of the equation is asymptotically stable our results improve and generalize the known ones in this direction

a caratheodory theorem for the bidisk via hilbert space methods if is an analytic function bounded by 1 on the bidisk mathbb d 2 and tau in partial mathbb d 2 is a point at which has an angular gradient nabla varphi tau then nabla varphi lambda to nabla varphi tau as nontangentially in mathbb d 2 this is an analog for the bidisk of a classical theorem of caratheodory for the disk for as above if tau in partial mathbb d 2 is such that the lim inf of 1 varphi lambda 1 lambda as is finite then the directional derivative d exists for all appropriate directions delta in mathbb c 2 moreover one can associate with and an analytic function h in the pick class such that the value of the directional derivative can be expressed in terms of h

stability in functional differential equations established using fixed point theory abstract in this paper we consider a nonlinear scalar delay differential equation with variable delays and give some new conditions for the boundedness and stability by means of krasnoselskii s fixed point theory a stability theorem with a necessary and sufficient condition is proved the results in t a burton stability by fixed point theory or liapunov s theory a comparison fixed point theory 4 2003 15 32 t a burton t furumochi asymptotic behavior of solutions of functional differential equations by fixed point theorems dynamic systems and applications 11 2002 499 519 b zhang fixed points and stability in differential equations with variable delays nonlinear analysis 63 2005 e233 e242 are improved and generalized some examples are given to illustrate our theory

operator monotone functions and lowner functions of several variables we prove generalizations of lowner s results on matrix monotone functions to several variables we give a characterization of when a function of d variables is locally monotone on d tuples of commuting self adjoint n by n matrices we prove a generalization to several variables of nevanlinna s theorem describing analytic functions that map the upper half plane to itself and satisfy a growth condition we use this to characterize all rational functions of two variables that are operator monotone

fixed points and stability in differential equations with variable delays abstract in this paper we consider a linear scalar differential equation with variable delays and give conditions to ensure that the zero solution is asymptotically stable by means of fixed point theory these conditions do not require the boundedness of delays nor do they ask for a fixed sign on the coefficient functions an asymptotic stability theorem with a necessary and sufficient condition is proved

improved stability conditions for a class of stochastic volterra levin equations in this paper we study the mean square asymptotic stability of a class of generalized nonlinear stochastic volterra levin equations by using fixed point theory several sufficient conditions are established for ensuring that the equation is mean square asymptotically stable as well as exponentially stable the main results are new which generalize and improve some well known results in burton 2006 4 and luo 2010 18 finally two examples are given to illustrate our results

stability analysis of neutral stochastic delay differential equations by a generalisation of banach s contraction principle abstractin this paper we consider a class of neutral stochastic differential systems with variable delays and give sufficient conditions to ensure that the zero solution is asymptotically stable in the mean square by means of a generalisation of banach s contraction principle these conditions do not require the boundedness of delays nor do they ask for a fixed sign on the coefficient functions the results are shown to improve the previous globally stable results derived in the literature

fixed points and exponential stability for stochastic volterra levin equations in this paper we study a stochastic volterra levin equation by using fixed point theory we give some conditions for ensuring that this equation is exponentially stable in mean square and is also almost surely exponentially stable our result generalizes and improves on the results in 14 1 30

stability of an integro differential equation in this work we study a scalar integro differential equation and give some new conditions ensuring that the zero solution is asymptotically stable by means of the fixed point theory our work extends and improves the results in the literature

power boundedness and similarity to contractions for some perturbations of isometries the relation between power boundedness and similarity to a contraction has been thoroughly investigated by cassier 1999 for a certain class of operators on hilbert space we explore the application of those results to one dimensional perturbations of the shift operator the criteria obtained lead to various connections with function theory problems

the boundedness and stability of neutral delay differential equations with damped stochastic perturbations via fixed point theory in this paper a class of neutral stochastic differential equation is studied by using the fixed point method some conditions are established for ensuring the equation is bounded asymptotically stable and j c stable in mean square then with borel cantelli lemma several sufficient conditions for almost surely asymptotic stability and j c stability are given the conditions do not require the boundedness of delays nor do they ask for the continuousness on the coefficient functions the results of this paper are new and they extend and improve previously known results

stability results for neutral stochastic functional differential equations via fixed point methods in this paper we prove some results on the mean square asymptotic stability of a class of neutral stochastic differential systems with variable delays by using a contraction mapping principle name

a polynomially bounded operator on hilbert space which is not similar to a contraction let e 0 we prove that there exists an operator te e2 2 such that for any polynomial p we have iip te ii not similar to a contraction i e there does not exist an invertible operator s f2 e f2 such that jis 1tesii tributed to halmos after his well known 1970 paper ten problems in hilbert space we also give some related finite dimensional estimates department of mathematics texas a m university college station texas 77843 universite paris vi equipe d7analyse case 186 75252 paris cedex 05 france e mail address gipqccr jussieu fr this content downloaded from 157 55 39 104 on sun 19 jun 2016 06 52 47 utc all use subject to http about jstor org terms

stability of linear neutral differential equations with delays and impulses established by the fixed points method abstract in this paper we consider the impulsive effects on the stability of the zero solution of the linear neutral differential equations with variable delays by transforming the equations into ones without impulses and using fixed point theory some sufficient conditions for asymptotic stability and exponential stability of the zero solution are obtained the paper extends and improves results on sufficient conditions obtained by jin and luo 2008 17 and ardjouni and djoudi 2011 18 which is shown clearly in example 1 this paper also shows that the impulse intensity and the impulse time both influence the decay rate of the convergence to zero of the solutions finally two examples are given to show applications of some results obtained