on the stability of the functional equation f x y xy f x f y xf y yf x abstract in this paper we study the hyers ulam stability and the superstability of the functional equation f x y xy f x f y xf y yf x

a fixed point theorem and the hyers ulam stability in non archimedean spaces abstract we prove a fixed point theorem in complete non archimedean normed spaces and show its applications in the hyers ulam stability of some functional equations

a linear programming approach to the synthesis of fixed structure controllers this paper describes a new approach to the synthesis of fixed structure and fixed order controllers such controllers are required in many practical applications a broad class of fixed structure controller synthesis problems can be reduced to the determination of a real controller parameter vector or simply a controller k k 1 k 2 k t so that a given set of real or complex polynomials of the form p s k po s k 1 p 1 s k t p t s is hurwitz the stability of the closed loop system requires a real characteristic polynomial to be hurwitz while several performance criteria can be satisfied by ensuring that a family of complex polynomials is hurwitz a novel feature of this paper is the exploitation of the interlacing property ip of hurwitz polynomials to construct arbitrarily tight approximations of the set of stabilizing controllers this is done by systematically constructing sets of linear inequalities in k the union of the feasible sets of linear inequalities provides an approximation of the set of all controllers k which render p s k hurwitz as the number of sets of linear inequalities increases and approaches infinity we show that the union of the feasible sets approaches the set of all stabilizing controllers of the desired structure the main tools that are used in the construction of the sets of linear inequalities are the hermite biehler theorem descartes rule of signs and its generalization we provide examples of the applicability of the proposed methodology to the synthesis of fixed order stabilizing controllers

interactive image segmentation based on synthetic graph coordinates in this paper we propose a framework for interactive image segmentation the goal of interactive image segmentation is to classify the image pixels into foreground and background classes when some foreground and background markers are given the proposed method minimizes a min max bayesian criterion that has been successfully used on image segmentation problem and it consists of several steps in order to take into account visual information as well as the given markers without any requirement of training first we partition the image into contiguous and perceptually similar regions superpixels then we construct a weighted graph that represents the superpixels and the connections between them an efficient algorithm for graph clustering based on synthetic coordinates is used yielding an initial map of classified pixels this method reduces the problem of graph clustering to the simpler problem of point clustering instead of solving the problem on the graph data structure as most of the known algorithms from literature do finally having available the data modeling and the initial map of classified pixels we use a markov random field mrf model or a flooding algorithm to get the image segmentation by minimizing a min max bayesian criterion experimental results and comparisons with other methods from the literature are presented on lhi gulshan and zhao datasets demonstrating the high performance and accuracy of the proposed scheme

stability of a functional equation deriving from cubic and quadratic functions abstract in this paper we establish the general solution of the functional equation 6 f x y 6 f x y 4 f 3 y 3 f x 2 y 3 f x 2 y 9 f 2 y and investigate the hyers ulam rassias stability of this equation

on stability of a functional equation with n variables abstract generalized hyers ulam stability problems of the quadratic functional equation f i 1 n x i n 2 i 1 n f x i 1 i j n f x i x j shall be treated under the approximately even or odd condition and some behaviors of quadratic mappings and additive mappings shall be investigated

on an equation characterizing multi additive quadratic mappings and its hyers ulam stability in this paper we unify the system of functional equations defining a multi additive quadratic mapping to obtain a single equation we also prove using the fixed point method the generalized hyers ulam stability of this equation thus generalizing some known results

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 hyers ulam stability of the functional equations that have the quadratic property abstract the hyers ulam stability of the quadratic functional equation 1 on a restricted domain shall be investigated and the result shall be applied to the study of an asymptotic behavior of that equation furthermore the hyers ulam stability problems of another quadratic equation 4 on a restricted domain shall also be treated under the approximately even or odd condition and some asymptotic behaviors of the quadratic mappings and the additive mappings shall be investigated

on a cauchy jensen functional equation and its stability abstract in this paper we obtain the general solution and stability of the cauchy jensen functional equation 2 f x y z w 2 f x z f x w f y z f y w

a fixed point method for perturbation of bimultipliers and jordan bimultipliers in c ternary algebras let a be a c ternary algebra a c bilinear t a a a is called a c ternary algebra bi multiplier if it satisfies t abc d t a b cd t a bcd abt c d for all a b c d a also the mapping t a a a is a called c ternary algebra jordan bimultiplier if it satisfies t aaa a t a a aa t a aaa aat a a for all a a using the fixed point method we investigate the generalized hyers ulam rassias stability of bimultipliers and jordan bimultipliers in c ternary algebras the concept of hyers ulam rassias stability originated from the th m rassias stability theorem that appeared in his paper th m rassias proc am math soc 72 297 1978

a fixed point technique for investigating the stability of α β γ derivations on lie c algebras abstract we apply a fixed point theorem to investigate some new stability results for derivations on lie c algebras associated with the generalized cauchy jensen type additive functional equation i 1 n f x i 1 n 1 j 1 j i n x j 2 i 1 n f x i

random exploration of the procedural space for single view 3d modeling of buildings in this paper we tackle the problem of 3d modeling for urban environment using a modular flexible and powerful approach driven from procedural generation to this end typologies of architectures are modeled through shape grammars that consist of a set of derivation rules and a set of shape dictionary elements appearance from statistical point of view with respect to the individual pixel s properties of the dictionary elements is then learned using a set of training images image classifiers are trained towards recovering image support with respect to the semantics then given a new image and the corresponding footprint the modeling problem is formulated as a search of the space of shapes that can be generated on the fly by deriving the grammar on the input axiom defining an image based score function for the produced instances using the trained classifiers the best rules are selected making sure that we keep exploring the space by allowing some rules to be randomly selected new rules are then generated by resampling around the selected rules at the finest level these rules define the 3d model of the building promising results on complex and varying architectural styles demonstrate the potential of the presented method

on the stability of functional equations in banach spaces the paper is devoted to some results on the problem of s m ulam for the stability of functional equations in banach spaces the problem was posed by ulam 60 years ago

generalized hyers ulam rassias stability of n sesquilinear quadratic mappings on banach modules over c algebras assume that x is a left banach module over a unital c algebra a it is shown that almost every n sesquilinear quadratic mapping h xxxxx n a is an n sesquilinear quadratic mapping when h rx y z 1 z n h x ry z 1 z n h x y rz 1 z 2 z n h x y z 1 z 2 rz n rh x y z 1 z 2 z n r 0 r 1 holds for all x y z 1 z email protected x moreover we prove the generalized hyers ulam rassias stability of an n sesquilinear quadratic mapping on a left banach module over a unital c algebra

on the cauchy rassias stability of a generalized additive functional equation let x and y be banach spaces and f x y an odd mapping we solve the following generalized additive functional equation rf j 1dxjr j 0 1 j 1d j lrf j 1d 1 j xjr cld 1 cl 1d 1 1 j 1df xj for all x1 xd x moreover we deal with the above functional equation in banach modules over a c algebra and obtain generalizations of the cauchy rassias stability the concept of cauchy rassias stability for the linear mapping was originated from th m rassias s stability theorem that appeared in his paper th m rassias on the stability of the linear mapping in banach spaces proc amer math soc 72 1978 297 300

a fixed point approach to stability of functional equations abstract we prove a simple fixed point theorem for some not necessarily linear operators and derive from it several quite general results on the stability of a very wide class of functional equations in single variable

on the complete instability of interval polynomials abstract in this paper we study complete instability of interval polynomials which is the counterpart of classical robust stability that is the objective is to check if all polynomials in the family are unstable if not a subsequent goal is to find a stable polynomial to this end we first propose a randomized algorithm which is based on a recursive necessary condition for hurwitz stability the second contribution of this paper is to provide a probability one estimate of the volume of stable polynomials these results are based on a combination of deterministic and randomized methods finally we present two numerical examples and simulations showing the efficiency of the proposed methodology for small and medium size problems

self calibration of a moving camera from pointcorrespondences and fundamental matrices we address the problem of estimating three dimensional motion and structure from motion with an uncalibrated moving camera we show that point correspondences between three images and the fundamental matrices computed from these point correspondences are sufficient to recover the internal orientation of the camera its calibration the motion parameters and to compute coherent perspective projection matrices which enable us to reconstruct 3 d structure up to a similarity in contrast with other methods no calibration object with a known 3 d shape is needed and no limitations are put upon the unknown motions to be performed or the parameters to be recovered as long as they define a projective camera the theory of the method which is based on the constraint that the observed points are part of a static scene thus allowing us to link the intrinsic parameters and the fundamental matrix via the absolute conic is first detailed several algorithms are then presented and their performances compared by means of extensive simulations and illustrated by several experiments with real images

a generalization of the hyers ulam rassias stability of approximately additive mappings abstract in this paper we prove a generalization of the stability of approximately additive mappings in the spirit of hyers ulam and rassias

using extremal boundaries for 3 d object modeling the extremal boundaries of 3 d curved objects are the images of special curves drawn on the object and are called rims they are viewpoint dependent and characterized by the fact that the optical rays of their points are tangential to the surface of the object the mathematics of the relationship between the extremal boundaries and the surface of the object is studied this study makes it possible to design an algorithm for detecting those boundaries in the images that are likely to be extremal once this has been done one can reconstruct the rims and compute the differential properties of the surface of the object along them up to the second order if a qualitative description is sufficient the sign of the gaussian curvature of the surface along the rim can be computed in a much simpler way experimental results are presented on synthetic and real images the work provides a better understanding of the relationship between the apparent and real shape of a 3 d object as well as algorithms for reconstructing the local shape of such an object along the rims

on a problem of g isac and th m rassias concerning the stability of mappings abstract we give an answer to a problem of g isac and th m rassias concerning hyers ulam rassias stability of the linear mappings a new characterization of additive mappings is also given

isomorphisms between c ternary algebras in this paper we prove the hyers ulam rassias stability of homomorphisms in c ternary algebras and of derivations on c ternary algebras for the following generalized cauchy jensen additive mapping 2f j 1pxj2 j 1dyj j 1pf xj 2 j 1df yj this is applied to investigate isomorphisms between c ternary algebras the concept of hyers ulam rassias stability originated from the rassias stability theorem that appeared in his paper on the stability of the linear mapping in banach spaces see proc amr math soc 72 297 300 1978

on the stability of an n dimensional cubic functional equation abstract let n 2 be an integer number in this paper we investigate the generalized hyers ulam rassias stability in banach spaces and also banach modules over a banach algebra and a c algebra and the stability using the alternative fixed point of an n dimensional cubic functional equation in banach spaces f j 1 n 1 x j 2 x n f j 1 n 1 x j 2 x n j 1 n 1 f 2 x j 2 f j 1 n 1 x j 4 j 1 n 1 f x j x n f x j x n

stability of a functional equation deriving from quadratic and additive functions in quasi banach spaces abstract in this paper we establish the general solution of the functional equation f 2 x y f 2 x y f x y f x y 2 f 2 x 2 f x and investigate the hyers ulam rassias stability of this equation in quasi banach spaces

a new parameterization of stable polynomials in this note we develop a new characterization of stable polynomials specifically given n positive ordered numbers frequencies we develop a procedure for constructing a stable degree n monic polynomial with real coefficients this construction can be viewed as a mapping from the space of n ordered frequencies to the space of stable degree n monic polynomials the mapping is one one and onto thereby giving a complete parameterization of all stable degree n monic polynomials we show how the result can be used to generate parameterizations of stabilizing fixed order proper controllers for unity feedback systems we apply these results in the development of stability margin lower bounds for systems with parameter uncertainty

asymptotic behavior of generalized derivations on c algebras with applications we consider generalized derivations on c algebra and we will first study the conditions for a linear generalized derivation on c algebra then we prove some theorems involving approximate linear generalized derivations on c algebra so approximate linear generalized derivations on c algebra are characterized

a functional equation having monomials as solutions for each n 1 2 3 we obtain the general solution and the stability of the functional equation f 2x y f 2x y 2 n 2 f x y f x y 6f x and we obtain the general solution and the stability of the functional equation f 2x y f 2x y 6f y 4 f x y f x y 6f x using the fixed point method we prove the generalized hyers ulam stability of these functional equations

on the hyers ulam rassias stability of an additive functional equation in quasi banach spaces abstract in this paper we investigate the hyers ulam rassias stability of the following functional equation i 1 m f m x i j 1 j i m x j f i 1 m x i 2 f i 1 m m x i m n m 2 in quasi banach spaces

variational principles surface evolution pdes level set methods and the stereo problem we present a novel geometric approach for solving the stereo problem for an arbitrary number of images spl ges 2 it is based upon the definition of a variational principle that must be satisfied by the surfaces of the objects in the scene and their images the euler lagrange equations that are deduced from the variational principle provide a set of partial differential equations pdes that are used to deform an initial set of surfaces which then move toward the objects to be detected the level set implementation of these pdes potentially provides an efficient and robust way of achieving the surface evolution and to deal automatically with changes in the surface topology during the deformations i e to deal with multiple objects results of an implementation of our theory also dealing with occlusion and visibility are presented on synthetic and real images

on fuzzy approximately cubic type mapping in fuzzy banach spaces abstract the first study of the fuzzy approximately cubic mappings in nonlinear analysis is due to mirmostafaee and moslehian 2008 and a fuzzy version of a generalized hyers ulam rassias type stability for the cubic functional equation in the fuzzy normed linear space setting is presented in this note we give an alternative proof of this result using the fixed point method in probabilistic metric spaces moreover we investigate fuzzy generalized hyers ulam rassias stability of an n dimensional cubic type functional equation in fuzzy banach spaces

isomorphisms between c ternary algebras abstract in this paper we prove the hyers ulam rassias stability of homomorphisms in c ternary algebras and of derivations on c ternary algebras for the following cauchy jensen additive mappings 0 1 f x y 2 z f x y 2 z f x 2 f z 0 2 f x y 2 z f x y 2 z f y 0 3 2 f x y 2 z f x f y 2 f z these are applied to investigate isomorphisms between c ternary algebras the concept of hyers ulam rassias stability originated from the th m rassias stability theorem that appeared in his paper th m rassias on the stability of the linear mapping in banach spaces proc amer math soc 72 1978 297 300

fixed points of a mapping and hyers ulam stability abstract we show that many general results on hyers ulam stability of some functional equations in a single variable follow immediately from a simple fixed point theorem the theorem is formulated for self maps of some subsets of the space of functions from a nonempty set into the set of reals we also give some applications of that theorem e g in investigations of solutions of some difference equations and functional inequalities

on the hyers ulam rassias stability of a quadratic functional equation abstract in this paper we investigate the hyers ulam rassias stability problems of a new quadratic functional equation f x y z f x f y f z f x y f y z f z x furthermore the stability results will be applied to the study of an interesting asymptotic property of the quadratic functions

a fixed point approach to the stability of functional equations in non archimedean metric spaces abstract in this note we prove a simple fixed point theorem for a special class of complete metric spaces namely complete non archimedean metric spaces which are connected with some problems coming from quantum physics p adic strings and superstrings we also show that this theorem is a very efficient and convenient tool for proving the hyers ulam stability of a quite wide class of functional equations in a single variable

on the generalized hyers ulam stability of module left derivations let a be a unital normed algebra and let m be a unitary banach left a module if f a m is an approximate module left derivation then f a m is a module left derivation moreover if m a is a semiprime unital banach algebra and f tx is continuous in t r for each fixed x in a then every approximately linear left derivation f a a is a linear derivation which maps a into the intersection of its center z a and its jacobson radical rad a in particular if a is semisimple then f is identically zero

stability for the functional equation of cubic type abstract in this article we establish the stability of the orthogonally cubic type functional equation 1 2 for all x 1 x 2 x 3 with x i x j i j 1 2 3 where is the orthogonality in the sense of ratz and investigate the stability of the n dimensional cubic type functional equation 1 3 where n 3 is an integer

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

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

hyers ulam rassias stability of homomorphisms in quasi banach algebras associated to the pexiderized cauchy functional equation abstract in this paper we prove the hyers ulam rassias stability of homomorphisms in quasi banach algebras associated to the pexiderized cauchy functional equation this is applied to investigate homomorphisms between quasi banach algebras the concept of hyers ulam rassias stability originated from th m rassias stability theorem that appeared in his paper th m rassias on the stability of the linear mapping in banach spaces proc amer math soc 72 1978 297 300

hyers ulam rassias stability of an equation of davison abstract in this work the hyers ulam rassias stability of the davison functional equation f xy f x y f xy x f y is proved

the generalized hyers ulam rassias stability of a cubic functional equation abstract in this paper we obtain the general solution and the generalized hyers ulam stability for a cubic functional equation f 2x y f 2x y 2f x y 2f x y 12f x

an elementary proof of kharitonov s stability theorem with extensions gives an elementary proof of kharitonov s theorem using simple complex plane geometry without invoking the hermite bieler theorem kharitonov s theorem is a stability result for classes of polynomials defined by letting each coefficient vary independently in an arbitrary interval the result states that the whole class is hurwitz if and only if four special well defined polynomials are hurwitz the paper also gives elementary proofs of two previously known extensions for polynomials of degree less than six the requirement is reduced to fewer than four polynomials and the theorem is generalized to polynomials with complex coefficients