on the best constant in hyers ulam stability of some positive linear operators abstract we obtain the infimum of the hyers ulam stability constants for stancu bernstein and kantorovich operators and prove that in a class of certain positive linear operators this infimum for bernstein operator has a minimality property

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

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

estimation of a density from an imperfect simulation model uncertainty quantification of a technical system can be done using density estimation we usually start with a stochastic model which is fitted to the technical system and the density estimation is done using data from this stochastic model however in any application such a stochastic model will not be perfect and the estimation of the density should take into account the inadequacy of the stochastic model in this paper we show how observed data of the real system together with an imperfect simulation model can be used to derive confidence bands for the density of the technical system our main result is that the newly introduced confidence bands allow to derive lower and upper bounds on the probability of intervals in the technical system furthermore we present an upper bound on the area of the confidence band in case of a smooth density the results are illustrated by applying the estimates to simulated and real data

nonparametric regression estimation using penalized least squares we present multivariate penalized least squares regression estimates we use vapnik chervonenkis see statistical learning theory 1998 theory and bounds on the covering numbers to analyze convergence of the estimates we show strong consistency of the truncated versions of the estimates without any conditions on the underlying distribution

the 3 2 mixed refined zigzag theory for generally laminated beams theoretical development and c0 finite element formulation abstract a third order refined zigzag theory for multilayered composite and sandwich beams is developed based on the reissner mixed variational theorem the assumed kinematics enriches the timoshenko s beam theory a second and a third order smeared polynomial terms along with a piece wise linear contributions are added to the axial displacement whereas the transverse displacement is approximated with a power series expansion up to the second order term transverse shear and normal stress continuous and able to satisfy the boundary stress conditions on the outer beam surfaces are assumed by the model the transverse shear stress is derived with the aid of the elasticity equations whereas a third order power series expansion is adopted for the transverse normal stress based on the proposed model an efficient c 0 continuous beam element is formulated by adopting the anisoparametric interpolation strategy to avoid the shear locking phenomenon the accuracy of the proposed model and the finite element implementation is assessed by solving problems concerning the elasto static behavior of generally laminated beams both simply supported and clamped at the ends comparison with reference solution elasticity or high fidelity fe model demonstrates the remarkable accuracy of the proposed model both in terms of displacements and stresses distributions as well as the finite element implementation efficiency

no empirical probability measure can converge in the total variation sense for all distributions for any sequence of empirical probability measures n on the borel sets of the real line and any 0 there exists a singular continuous probability measure such that inf sup n 9m n a a a 1 2 almost surely

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

the equivalence of weak strong and complete convergence in l_1 for kernel density estimates theorem 1 let k be a nonnegative borel measurable function on rd with f k x dx 1 then the following conditions are equivalent i j 0 in probability as n oo some f ii jn o 0 in probability as n s oo all f iii jn s 0 almost surely as n oo all f iv jn 0 exponentially as n oc i e for all e 0 there exist r no 0 such that p jne no all f v lim0h 0 and limnnhd oo also v implies iv when k is merely absolutely integrable and f k x dx 1 0

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

complete stress field in sandwich panels with a new triangular finite element of single layer theory abstract an alternative to conventional three dimensional solid elements or elements based on the layerwise zig zag theory is an element based on a single layer plate theory in which the weighted average field variables capture the panel displacement and stress fields this study presents a new triangular finite element for modeling thick sandwich panels based on a 3 2 order single layer plate theory it utilizes seven weighted average field variables arising from the cubic and quadratic representations of the in plane and transverse displacement fields respectively in order to satisfy the c1 interelement continuity requirement this triangular sandwich element is developed by utilizing the hybrid energy functional

consistency of orthogonal series density estimators based on grouped observations in this correspondence we show that nonparametric orthogonal series estimators of probability densities retain the mean integrated square error mise consistency when observations are grouped to the points of a uniform grid prebinned this kind of grouping is typical for computer rounding errors and may also be useful in data compression before calculating estimates e g using the fft the main result shows that mise consistency holds for all square integrable densities under mild conditions on the grid step size

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

adaptive density estimation from data with small measurement errors in this paper we study the problem of density estimation from data that contains small measurement errors the only assumption on these errors is that the maximal measurement error is bounded by some real number converging to zero for sample size tending to infinity in particular we do not assume that the measurement errors are independent with expectation zero we estimate the density by a standard kernel density estimate applied to data with measurement errors and derive a data driven method to choose its bandwidth we derive an adaptation result for this estimate and analyze the expected l 1 error of our density estimate depending on the smoothness of the density and the size of the maximal measurement error the results are applied in a density estimation problem in a simulation model where we show under suitable assumptions that the l 1 error of our newly proposed estimate converges to zero much faster than the l 1 error of the standard kernel density estimate if both are based on the same number of observations in the simulation model the performance of the method in case of finite sample size is analyzed using simulated data

remarks on stability and non stability of the linear functional equation of the first order abstract we prove some results on stability and non stability of the linear functional equation of the first order in single variable moreover we suggest some possible definitions of stability and non stability

hierarchic models for laminated composites the principles governing the formulation of hierarchic models for laminated composites are discussed the essential features of the hierarchic models described herein are a the exact solutions corresponding to the hierarchic sequence of models converge to the exact solution of the corresponding problem of elasticity for a fixed laminate thickness and b the exact solution of each model converges to the same limit as the exact solution of the corresponding problem of elasticity with respect to the laminate thickness approaching zero hierarchic models make the computation of any engineering data possible to an arbitrary level of precision within the framework of the theory of elasticity examples are presented

nonparametric density estimation the l 1 view differentiation of integrals consistency lower bounds for rates of convergence rates of convergence in l1 the automatic kernel estimate l1 and pointwise convergence estimates related to the kernel estimate and the histogram estimate simulation inequalities and random variate generation the transformed kernel estimate applications in discrimination operations on density estimates estimators based on orthogonal series index

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

rates of convergence of minimum distance estimators and kolmogorov s entropy on construit des estimateurs robustes et on montre que le taux de convergence resultant depend naturellement d une fonction entropie

analysis of thick sandwich construction by a 3 2 order theory abstract this study is an extension of the 1 2 order plate theory to a higher order 3 2 theory based on the equivalent single layer assumptions the in plane and transverse displacement components are expressed as cubic and quadratic expansions through the thickness of the sandwich construction also the transverse stress component is assumed to vary as a cubic function through the thickness utilizing reissner s definitions for kinematics of thick plates the displacement components at any point on the plate are approximated in terms of weighted average quantities displacements and rotations that are functions of the in plane coordinates the undetermined coefficients defining the in plane and transverse displacement fields are then expressed in terms of the weighted average displacements and rotations and their derivatives by directly employing reissner s definitions and enforcing the zero transverse shear stress conditions on the upper and lower surfaces of the sandwich panel the coefficients defining the transverse stress component are obtained by requiring the transverse strain component which is expressed in terms of the unknown coefficients of the transverse stress component from a mixed constitutive relation to be the least squares equivalent of the kinematic definition of the transverse strain component the resulting expressions for the unknown coefficients of the transverse stress component are related to resultant strains and curvatures defined from kinematic relations the equations of equilibrium and boundary conditions of the sandwich plate based on the 3 2 higher order theory are derived by employing the principles of virtual displacements the robustness and accuracy of this 3 2 order plate theory are established through comparisons with exact solutions available in the literature the finite element implementation of the present 3 2 order plate theory is also discussed

computational homogenisation of composite plates consideration of the thickness change with a modified projection strategy in the present paper a method for the modelling of the mechanical behaviour of composite plates especially hybrid laminates and sandwich plates is proposed the chosen method is the computational homogenisation or the so called fe 2 for plates the principle is to split the considered problem into two scales on the one hand the two dimensional fe computation of a plate is performed on the macroscale on the other hand a three dimensional fe problem is computed on the mesoscale which enables the discretisation of the layers organisation from each integration point of the macroscale the deformations are projected to the representative volume element rve on the mesoscale where a dirichlet boundary value problem is solved finally the homogenisation of the stresses is conducted to define the stress resultants of the macroscale the proposed method presents the advantage to take into account any material behaviour without any transformation of the constitutive laws even non linear ones furthermore the new projection strategy presented in this work considers the thickness change of the plate which enables a resolution of the poisson locking the method is illustrated by the simulation of the mechanical behaviour of both sandwich plate and of hybrid laminate

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

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

a 1 2 order theory for elastodynamic analysis of thick orthotropic shells abstract a higher order shell theory is developed for elastodynamic analysis of orthotropic shells the theory accounts for all basic deformations including transverse shear and transverse normal strains and stresses the theory is developed in orthogonal curvilinear coordinates in which the reference surface components of the displacement vector vary linearly through the thickness while the transverse displacement is parabolic transverse shear and transverse normal strains are formulated to satisfy physical traction conditions at the top and bottom shell surfaces and are also made least squares compatible with the corresponding strains that are derived directly from the strain displacement relations of three dimensional elasticity in these variational statements of strain compatibility transverse shear and transverse normal correction factors are introduced and are determined from dynamic considerations in the manner originally proposed by mindlin equations of motion and associated engineering poisson boundary conditions are derived from a three dimensional variational principle an important feature of the present theory is the requirement of only simple c0 and c 1 continuity for the shell kinematic variables this aspect makes the theory particularly attractive for the development of efficient shell finite elements suitable for general purpose finite element analysis of thick shell structures analytical solutions for the free vibration of isotropic and orthotropic cylindrical shells are obtained for a wide range of thickness radius and thickness wavelength ratios and found to be in close agreement with the exact elasticity solutions

nonparametric estimation via empirical risk minimization a general notion of universal consistency of nonparametric estimators is introduced that applies to regression estimation conditional median estimation curve fitting pattern recognition and learning concepts general methods for proving consistency of estimators based on minimizing the empirical error are shown in particular distribution free almost sure consistency of neural network estimates and generalized linear estimators is established

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

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

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

on approximate solutions of the linear functional equation of higher order abstract we show that under some assumptions every approximate solution of the linear functional equation of higher order in single variable generates a solution of the equation that is close to it we also give a description of a procedure that yields such a solution estimate the distance between those approximate and exact solutions to the equation and discuss the problem of uniqueness moreover as a consequence we obtain some results concerning the hyers ulam stability of the equation

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

ultra high frequency volatility estimation with dependent microstructure noise we analyze the impact of time series dependence in market microstructure noise on the properties of estimators of the integrated volatility of an asset price based on data sampled at frequencies high enough for that noise to be a dominant consideration we show that combining two time scales for that purpose will work even when the noise exhibits time series dependence analyze in that context a refinement of this approach is based on multiple time scales and compare empirically our different estimators to the standard realized volatility

vibration of thick laminated composite plates abstract two versions of a 1 2 higher order laminate plate theory are derived for elastodynamics and used to compute natural frequencies and mode shapes for homogeneous and laminated plates the theories include deformations due to transverse shear and transverse normal stretching and account for rotary and thickness motion inertia analytic natural frequencies and mode shapes are obtained for thin and thick orthotropic and laminated simply supported plates and compared with exact solutions of three dimensional elasticity the higher and first order shear deformable theories and the classical laminate plate theory both versions of the present theory are shown to provide improved accuracy over other approximate theories when compared to elasticity theory particularly for thick laminates and high frequency modes the theory also accurately predicts the lowest thickness stretch frequencies which cannot be obtained with first order shear deformable theories from the computational perspective the theory is especially well suited for generating simple and efficient displacement finite elements based on conventionalc0 continuous displacements and five degrees of freedom at each boundary node an approximation scheme for a three noded triangular plate element is also discussed together with a numerical study demonstrating the element performance in relation to two commercial plate elements

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 approximate isometries and application to stability of a functional equation abstract in this paper we show a generalized stability of isometries between banach spaces making use of this result we prove the corresponding stability of the functional equation f x y f x f y

on arbitrarily slow rates of global convergence in density estimation let a density f on rd be estimated by fn x x1 xn where x rd fn is a borel measurable function of its arguments and x1 xn are independent random vectors with common density f let p 1 be a constant one of the main results of this note is that for every sequence fn and for every positive number sequence an satisfying lim an 0 there exists an f such that e left smallint f n left x right f left x right p dx right a n infinitely often

an improved plate theory of 1 2 order for thick composite laminates abstract a new two dimensional laminate plate theory is developed for the linear elastostatic analysis of thick composite plates the theory employs equivalent single layer assumptions for the displacements transverse shear strains and transverse normal stress the inplane and transverse displacements are respectively linear and quadratic expansions through the laminate thickness where the low order expansion coefficients correspond to the variables of reissner s first order shear deformable theory the transverse shear strains and transverse normal stress are assumed to be quadratic and cubic respectively through the thickness they are expressed in terms of the kinematic variables of the theory by means of a least squares compatibility requirement for the transverse strains and explicit enforcement of exact traction boundary conditions on the top and bottom plate surfaces application of the virtual work principle results in the loth order equations of equilibrium and associated poisson boundary conditions a major advantage of this theory over other higher order theories lies in its perfect suitability for finite element approximation simple c 0 continuous interpolations for the kinematic variables of the first order theory and optionally c 1 interpolations for the two higher order displacements are needed to formulate effective and robust two dimensional plate elements capable of full three dimensional ply by ply strain and stress recovery within the framework of general purpose finite element codes in assessing the predictive capability of the theory analytic solutions for the problem of cylindrical bending are derived and compared with exact three dimensional elasticity results and those of the earlier version of the 1 2 order plate theory

restatement of first order shear deformation theory for laminated plates abstract a restatement of the first order shear deformation theory of plates is offered and verified numerically by exact 3 d elasticity results based on a more appropriate physical assumption the restated theory innovatively interprets its variables and applies elasticity equations in a more pertinent manner it assumes physically that only in some average sense does a straight line originally normal to the midplane remain straight and rotate relative to the normal of the midplane after deformation hence the in plane displacement is still approximated in an average sense as linear and the transverse deflection as constant through the plate thickness the associated nominal uniform transverse shear strain directly derived from these displacement field assumptions is identified as the weighted average transverse shear strain through the plate thickness with the corresponding transverse shear stress as the weighting function while the actual transverse shear strain is permitted to vary through the thickness and satisfies the constitutive law with its stress counterpart likewise the average rotation of the line is identified as its weighted average value instead of the one evaluated from a linear regression of the inplane displacement with the least square method examination of bending energy and transverse shear energy supports this interpretation in addition an effective transverse shear stiffness parameter is identified and proven appropriate this restated first order shear deformation theory yields accurate local as well as global response predictions without employing a shear correction factor

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 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

generalized stability of the cauchy and the jensen functional equations on spheres abstract we study a generalized stability problem for cauchy and jensen functional equations satisfied for all pairs of vectors x y from a linear space such that x y or x y x y with a given function

on the strong universal consistency of nearest neighbor regression function estimates two results are presented concerning the consistency of the k nearest neighbor regression estimate we show that all modes of convergence in l 1 in probability almost sure complete are equivalent if the regression variable is bounded under the additional condition k log n we also obtain the strong universal consistency of the estimate

necessary and sufficient conditions for the pointwise convergence of nearest neighbor regression function estimates where v 1 v is a given probability vector and xt x yl x x x y x is a permutation of x1 i71 x y according to increasing values of ilxi x i x e r a when ixi xll h x j x l but i 1 and some constant c 0

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

a stability of the generalized sine functional equations abstract in this paper we will investigate the stability of the generalized pexiderized sine functional equation g x h y f x y 2 2 f x y 2 2