global asymptotic stability of a higher order rational difference equation abstract in this note we consider the following rational difference equation x n 1 f x n r 1 x n r k g x n m 1 x n m l 1 f x n r 1 x n r k g x n m 1 x n m l n 0 1 where f c 0 k 0 and g c 0 l 0 with k l 1 2 0 r 1 r k and 0 m 1 m l and the initial values are positive real numbers we give sufficient conditions under which the unique equilibrium x 1 of this equation is globally asymptotically stable which extends and includes corresponding results obtained in the recent literature

quadratic functional equations in a set of lebesgue measure zero abstract let r be the set of real numbers y a banach space and f r y we prove the hyers ulam stability theorem for the quadratic functional inequality f x y f x y 2 f x 2 f y for all x y where r 2 is of lebesgue measure 0 using the same method we dealt with the stability of two more functional equations in a set of lebesgue measure 0

global attractivity in a rational recursive sequence our aim in this paper is to investigate the periodic character invariant intervals and the global attractivity of all positive solutions of the nonlinear difference equationx n email protected email protected email protected n 1 n 0 1 where a 0 b c 0 we show that the positive equilibrium of the equation is a global attractor with a basin that depends on certain conditions posed on the coefficients

addendum to on the stability of functional equations on square symmetric groupoid abstract let x be a square symmetric groupoid and y d a complete metric divisible square symmetric groupoid in this paper we obtain the hyers ulam stability problem of functional inequality d g x y g x g y e x y for approximate mapping g x y of functional equation f x y f x f y differing by e x 2 0 in particular we have investigated the case of f x f y h f x 1 t f y 1 t on some set y

decomposition of mappings approximately inner product preserving abstract for hilbert spaces e and f we consider the class of mappings f e f preserving approximately inner product in the following sense f x f y x y x y x y e for suitable function we show that the orthogonal projection of f onto some closed linear subspace h of f is a linear isometry while the projection onto h is bounded by x x several consequences of such a decomposition are given in particular stability and superstability of inner product preserving mappings are considered

a note on robust pole assignment for periodic systems in this note a robust pole assignment algorithm is proposed for linear periodic discrete time systems with time varying dimensions of the state and or input spaces the algorithm deduces a periodic state feedback law by the minimization of the condition numbers of the eigenvector matrices of the closed loop system numerical examples are provided to show the performances of the algorithm

hyers ulam stability of functional equations with a square symmetric operation abstract the stability of the functional equation f x y h f x f y x y s is investigated where h is a homogeneous function and is a square symmetric operation on the set s the results presented include and generalize the classical theorem of hyers obtained in 1941 on the stability of the cauchy functional equation

stability of multi jensen mappings in non archimedean normed spaces in this paper we study the stability of the multi jensen mappings in non archimedean normed spaces the results improve and extend some recent results

a rational difference equation abstract we investigate the boundedness character the periodic nature and the global asymptotic stability of all positive solutions of the equation in the title with positive parameters and nonnegative initial conditions

continuous on rays solutions of an equation of the golab schinzel type abstract let x be a real linear space we characterize continuous on rays solutions f g x r of the equation f x g x y f x f y our result refers to papers of j chudziak 2006 14 and j brzd k 2003 11

on the quotient stability of a family of functional equations abstract we show some stability results for a family of functional equations that contains the exponential and the golab schinzel functional equations

on the generalized hyers ulam stability of multi quadratic mappings a mapping f v email protected w where v is a commutative group w is a linear space and n 2 is an integer is called multi quadratic if it is quadratic in each variable in this paper we prove the generalized hyers ulam stability of multi quadratic mappings in banach spaces and complete non archimedean spaces

on the hyers ulam stability of the linear differential equation abstract we obtain some results on generalized hyers ulam stability of the linear differential equation in a banach space as a consequence we improve some known estimates of the difference between the perturbed and the exact solutions

stability problem for the golab schinzel type functional equations let x be a vector space over a field k of real or complex numbers n n and k 0 we study the stability problem for the golab schinzel type functional equations f x f x ny f x f y in the class of functions f x k such that the set x x f x 0 has an algebraically interior point

on obtaining a realization of a polynomial matrix description of a system the computation of a state space realization of a linear dynamical system starting from a polynomial matrix description of it is addressed simple procedures are given for obtaining its dynamic matrix possibly in some canonical or block companion form through unimodular transformations starting from a square diagonal polynomial matrix obtained as an intermediate step of the overall realization algorithm

discrete time linear periodic realization in the frequency domain abstract given an appropriate collection of periodic rational matrices we characterize when it has a periodic realization the state space and the input output invariant formulation of discrete time periodic linear systems are involved

global attractivity of the recursive sequence xn 1 α βxn 1 γ xn our aim in this paper is to investigate the global attractivity of the recursive sequence x n 1 a bx n 1 c x n under specified conditions we show that the positive equilibrium point of the equation is a global attractor with a basin that depends on certain conditions posed on the coefficients

on the dynamics of the recursive sequence xn 1 xn 1β γxn 22xn 4 γxn 2xn 42 in this paper we investigate the global behavior of the difference equation x n 1 x n email protected email protected n 2 2x n email protected n 2x n 4 2 n 0 1 with positive parameters and non negative initial conditions

the space of psi gamma additive mappings on semigroups in this paper we introduce the concept of pseudoadditive mappings from a semigroup into a banach space and we provide a generalized solution of ulam s problem for approximately additive mappings

on solutions of a common generalization of the golab schinzel equation and of the addition formulae abstract under some additional assumptions we determine solutions of the equation f x m f x y f x f y where f r r is lebesgue measurable or baire measurable m r r and r 2 r all three functions are unknown

measure zero stability problem of a new quadratic functional equation abstract let r be the set of real numbers y a banach space and f r y we prove the ulam hyers stability theorem for the new quadratic functional equation j 2 k f x 1 x j f x 1 x j 2 k 1 f x 1 2 j 2 k f x j for all x 1 x k where r k is of lebesgue measure 0 using the result we obtain an asymptotic behavior of the equation

on the recursive sequence xn axn 1 bxn 2c dxn 1xn 2 in this paper we study the invariant intervals the global attractivity of the equilibrium points and the asymptotic behavior of the solutions of the difference equationx n ax n 1 bx n 2c dx n 1x n 2 n 1 2 where a 0 b c d 0

global asymptotic stability in a rational recursive sequence in this paper we study the global stability of the difference equationx n a bx n 1 cx n 1 2d x n 2 n 1 2 where a b 0 and c d 0 we show that one nonnegative equilibrium point of the equation is a global attractor with a basin that is determined by the parameters and every positive solution of the equation in the basin exponentially converges to the attractor

hyers ulam stability of the linear differential operator with nonconstant coefficients abstract we obtain some stability results for the linear differential operator of order one in banach spaces as a consequence we derive a result on hyers ulam stability for the linear differential operator of higher order with nonconstant coefficients

on the stability of a pexiderized gol ab schinzel equation in this paper we establish the stability of the pexiderized email protected b schinzel functional equation f x yf x g x h y under the condition that lim t 0h tx exists and is non zero

exponential type functional equation and its hyers ulam stability abstract we give the solution of the functional equation f x y f x f y x y under some conditions also we show its hyers ulam stability

general stability of functional equations of linear type making use of a dynamical systems notion called shadowing we prove a stability result for linear functional equations in metric groups as a corollary we obtain stability of the quadratic functional equation in the case when the target space is a metric group satisfying some local 2 divisibility condition

discrete time positive periodic systems with state and control constraints the aim of this technical note is to provide an efficient control design technique for discrete time positive periodic systems in particular stability positivity and periodic invariance of such systems are studied moreover the concept of periodic invariance with respect to a collection of boxes is introduced and investigated with connection to stability it is shown how such concept can be used for deriving a stabilizing state feedback control that maintains the positivity of the closed loop system and respects states and control signals constraints in addition all the proposed results can be efficiently solved in terms of linear programming

comments on the core of the direct method for proving hyers ulam stability of functional equations in this short paper the core of the direct method for proving stability of functional equations is described in a clear way and in a quite general form

christensen measurable solutions of some functional equation abstract let x be a separable f space over the field k of reals or complex numbers we characterize solutions of the equation f x m f x y f x f y in the class of functions m k k and christensen measurable functions f x k

necessary conditions for the general pole placement problem via constant output feedback a necessary condition is obtained for the simultaneous placement of a finite pole structure and an infinite pole structure of a linear system using constant output feedback the result can be applied to the general pole placement problem in singular systems using constant generalized state feedback

on the recursive sequences xn 1 αxn 1β xn our aim in this paper is to investigate the global attractivity of the recursive sequences x n 1 email protected n 1 b x n under specified conditions we show that the zero equilibrium points of these equations are global attractor with basin that depend on certain conditions posed on the coefficients

minimal periodic realizations of transfer matrices periodic controllers designed based on the so called lifting technique are usually represented by transfer matrices real operations require that the controllers be implemented as periodic systems the problem of realizing an nn sub o nn sub i proper rational transfer matrix as an n sub i input n sub o output n periodic discrete time system is studied an algorithm for obtaining periodic realizations which have a minimal number of states is proposed the result can also be used to remove any redundant states that exist in a periodic system

output feedback of forward backward periodic systems stability an n periodic forward backward system defined by a collection of nonproper rational matrices is considered in addition an n periodic collection of output feedbacks such that the closed loop system is n periodic and forward backward is constructed block ordered coprime factorizations of a rational matrix are used in the stabilization of that closed loop system

stability of functional equations in single variable abstract this paper discusses hyers ulam stability for functional equations in single variable including the forms of linear functional equation nonlinear functional equation and iterative equation surveying many known and related results we clarify the relations between hyers ulam stability and other senses of stability such as iterative stability continuous dependence and robust stability which are used for functional equations applying results of nonlinear functional equations we give the hyers ulam stability of bottcher s equation we also prove a general result of hyers ulam stability for iterative equations

on approximation of approximately linear mappings by linear mappings abstract assume a is a normed linear space b is a banach space and f a b is a mapping approximately linear we solve the following ulam problem give conditions in order for a linear mapping near an approximately linear mapping to exist

approximate ternary jordan derivations on banach ternary algebras let a be a banach ternary algebra over a scalar field r or c and x be a ternary banach a module a linear mapping d a a x x is called a ternary jordan derivation if d xxx a d x xx x xd x x x xxd x x for all x a in this paper we investigate ternary jordan derivations on banach ternary algebras associated with the following functional equation f x y z 4 f 3x y 4z 4 f 4x 3z 4 2f x moreover we prove the generalized ulam hyers stability of ternary jordan derivations on banach ternary algebras

stability of the multi jensen equation abstract in this paper we study the stability in the sense of th m rassias of multi jensen equation

on the recursive sequencexn 1 α xn 1 xn abstract we study the global stability the boundedness character and the periodic nature of the positive solutions of the difference equationxn 1 xn 1 xn where 0 and where the initial conditionsx 1andx0are arbitrary positive real numbers

the stability of a cubic type functional equation with the fixed point alternative abstract in this note we investigate the generalized hyers ulam rassias stability for the new cubic type functional equation f x y 2 z f x y 2 z f 2 x f 2 y 2 f x y 2 f x z 2 f x z 2 f y z 2 f y z by using the fixed point alternative the first systematic study of fixed point theorems in nonlinear analysis is due to g isac and th m rassias internat j math math sci 19 1996 219 228

observers for discrete singular systems the author considers the design of observers for the discrete singular system ex k 1 ax k bu k y k cx k placing special emphasis on the problems of state reconstruction and minimal time state reconstruction it is shown that for a singular system finite poles can be moved to infinity by state feedback and the state can be reconstructed by causal observers

stability of the recursive sequence xn 1 α βxn γ xn 1 abstract in this paper we investigate the global asymptotic stability of the recursive sequence xn 1 xn xn 1 n 0 1 where 0 we show that the unique positive equilibrium point of the equation is a global attractor with a basin that depends on the conditions posed on the coefficients

on the stability of the golab schinzel functional equation abstract motivated by the problem of r ger we consider the stability of the golab schinzel functional equation we show that in the class of functions satisfying some weak regularity assumption the equation is superstable

a simple procedure for the stabilization of a class of uncontrollable generalized systems this paper gives a simple procedure for the stabilization with a prescribed rate of convergence of the free motions of a class of possibly single input uncontrollable generalized continuous time time invariant linear systems preserving the impulse free property if any

the pexiderized golab schinzel functional equation let x be a linear space over a commutative field k we characterize a general solution f g h k x k of the pexiderized golab schinzel equation f x g x y h x k y as well as real continuous solutions of the equation

global attractivity in a recursive sequence in this paper we study the invariant intervals the globally attractivity of the two equilibrium points and the oscillatory behavior of the solutions of the difference equationx n ax n 1 bx n 2c x n 2 n 1 2 where a b c 0