on the hyers ulam rassias stability of approximately additive mappings abstract in this paper using an idea from the paper of p gvruta j math anal appl 184 1994 431 436 the results of th m rassias j math anal appl 158 1991 106 113 shall be generalized

ramanujan formula for the generalized stirling approximation abstract the aim of this paper is to improve ramanujan s formula for approximation of the factorial function starting from burnside s formula in contradistinction with the classical formula that starts from stirling s formula

some further generalizations of the hyers ulam rassias stability of functional equations abstract in this paper we study the hyers ulam rassias stability theory by considering the cases where the approximate remainder is defined by f x y f x f y x y x y g 1 f x y g x h y x y x y g 2 2f x y 1 2 f x f y x y x y g 3 where g is a certain kind of algebraic system e is a real or complex hausdorff topological vector space and f g h are mappings from g into e we prove theorems for the hyers ulam rassias stability of the above three kinds of functional equations and obtain the corresponding error formulas

on an n dimensional mixed type additive and quadratic functional equation in this paper we investigate the generalized hyers ulam stability of the functional email protected k 2 k n 01fx email protected i 2n 1 k ix i 2 n 1f x 1 2 n email protected i 2nf x i f x i 0for integer values of n such that n 2 where f is a function from a normed space x to a banach space y the solutions of the equation are called additive quadratic mappings

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

testing equality between sets of coefficients after a preliminary test for equality of disturbance variances in two linear regressions abstract in this paper we propose a two stage test which consists of testing equality of regression coefficients after a preliminary test for equality of disturbance variances in two linear regressions the optimal procedure of the two stage test is presented the sampling performance of the optimal two stage test is compared with that of the jayatissa test and with that of the size corrected wald test

a generalization of the hyers ulam rassias stability of the pexiderized quadratic equations abstract in this paper we prove the hyers ulam rassias stability by considering the cases that the approximate remainder is defined by f x y f x y 1 2g x 2g y x y f x y g x y 1 2h x 2k y x y where g is a group x is a real or complex hausdorff topological vector space and f g h k are functions from g into x

on the stability of a functional equation deriving from an inequality of popoviciu for convex functions abstract in this paper we solve the jensen type functional equation n n 2 k 2 f x 1 x n n n 2 k 1 i 1 n f x i k 1 i 1 k n f x i 1 x i k k deriving from an inequality of popoviciu for convex functions likewise we investigate the stability of this functional equation in the spirit of hyers ulam rassias and g vru

a generalization of the hyers ulam rassias stability of jensen s equation in this paper we prove a generalization of the stability of the jensen s equation in the spirit of hyers ulam rassias and g vruta

products and ratios for a bivariate gamma distribution we derive the distributions of p xy and w x x y and the corresponding moment properties when x and y follow a bivariate gamma distribution the expressions turn out to involve several special functions we also provide extensive tabulations of the percentage points associated with the two distributions these tables obtained using intensive computing power will be of use to practitioners of the bivariate gamma distribution

on the stability of a quadratic jensen type functional equation abstract in this paper we obtain the general solution of the quadratic jensen type functional equation 9f x y z 3 f x f y f z 4 f x y 2 f y z 2 f z x 2 and prove the stability of this equation in the spirit of hyers ulam rassias and g vruta

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 ulam hyers stability of first order differential systems with nonlocal initial conditions abstract in this paper we investigate the ulam hyers stability of first order differential systems with nonlocal initial conditions on compact intervals in w 1 1 0 k and on noncompact intervals in w w 1 2 0 with suitable weight function w the novelty consists in the simultaneous use of vectorial norms convergent to zero matrices sobolev spaces for studying the ulam hyers stability of equations with nonlocal conditions on noncompact intervals

generalized hyers ulam stability for general additive functional equations in quasi β normed spaces abstract in 1940 s m ulam proposed the famous ulam stability problem in 1941 d h hyers solved the well known ulam stability problem for additive mappings subject to the hyers condition on approximately additive mappings the first author of this paper investigated the hyers ulam stability of cauchy and jensen type additive mappings in this paper we generalize results obtained for jensen type mappings and establish new theorems about the hyers ulam stability for general additive functional equations in quasi normed spaces

confidence intervals for weighted sums of poisson parameters directly standardized mortality rates are examples of weighted sums of poisson rate parameters if the numbers of events are large then normal approximations can be used to calculate confidence intervals but these are inadequate if the numbers are small we present a method for obtaining approximate confidence limits for the weighted sum of poisson parameters as linear functions of the confidence limits for a single poisson parameter the unweighted sum the location and length of the proposed interval depend on the method used to obtain confidence limits for the single parameter therefore several methods for obtaining confidence intervals for a single poisson parameter are compared for single parameters and for weighted sums of parameters simulation suggests that the coverage of the proposed intervals is close to the nominal confidence levels the method is illustrated using data on rates of myocardial infarction obtained as part of the who monica project in augsburg federal republic of germany

on the generalized hyers ulam rassias stability of an n dimensional quadratic functional equation abstract in this paper we investigate the generalized hyers ulam rassias stability of an n dimensional quadratic functional equation f i 1 n x i 1 i j n f x i x j n i 1 n f x i n 2

generalization of functional equation for the square root spiral abstract in the paper we give the general solution of the linear functional equation p 1 p x c x h x furthermore we discuss its hyers ulam rassias stability and the stability in the sense of ger for the equation p 1 p x c x our results are applied to the square root spiral so that the related results by heuvers et al k j heuvers d s moak b boursaw the functional equation of the square root spiral in th m rassias ed functional equations and inequalities kluwer 2000 pp 111 117 and results by jung and sahoo stability of functional equation for square root spirals appl math lett 15 2002 435 438 are generalized

lie homomorphisms between lie c algebras and lie derivations on lie c algebras abstract we prove the generalized hyers ulam rassias stability of lie homomorphisms in lie c algebras and of lie derivations on lie c algebras

cauchy rassias stability of a generalized trif s mapping in banach modules and its applications abstract let x and y be vector spaces it is shown that a mapping f x y satisfies the functional equation 0 1 mn mn 2 c k 2 f x 1 x mn mn mn 2 c k 1 i 1 mn f x i x i m 1 m k 1 i 1 i k mn f x i 1 x i k k if and only if the mapping f x y is additive and we prove the cauchy rassias stability of the functional equation 0 1 in banach modules over a unital c algebra as an application we show that every almost homomorphism h a b of a unital c algebra a onto a unital c algebra b is a c algebra isomorphism when h 2 d uy h 2 d u h y for all unitaries u a all y a and d 0 1 2

stability of additive mappings in non archimedean fuzzy normed spaces in this paper we introduce a notion of a non archimedean fuzzy norm and study the stability of the cauchy equation in the context of non archimedean fuzzy spaces in the spirit of hyers ulam rassias gavruta as a corollary the stability of the jensen equation is established we indeed present an interdisciplinary relation between the theory of fuzzy spaces the theory of non archimedean spaces and the theory of functional equations

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

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

homomorphisms between c algebras and linear derivations on c algebras abstract it is shown that every almost unital almost linear mapping h a b of a unital c algebra a to a unital c algebra b is a homomorphism when h 3 n u y h 3 n u h y holds for all unitaries u a all y a and all n 0 1 2 and that every almost unital almost linear continuous mapping h a b of a unital c algebra a of real rank zero to a unital c algebra b is a homomorphism when h 3 n u y h 3 n u h y holds for all u v a v v v 1 and v is invertible all y a and all n 0 1 2 furthermore we prove the hyers ulam rassias stability of homomorphisms between unital c algebras and c linear derivations on unital c algebras the concept of hyers ulam rassias stability originated from the th m rassias stability theorem that appeared in his paper on the stability of the linear mapping in banach spaces proc amer math soc 72 1978 297 300

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 generalization of the hyers ulam rassias stability of the pexider equation in this paper we prove a generalization of the stability of the pexider equation f x y g x h y in the spirit of hyers ulam rassias and g vruta

two stage interference resistant adaptive periodically time varying cma blind equalization we consider the problem of blindly equalizing a digital communication signal distorted by a linear time invariant channel and contaminated by severe co channel or adjacent channel digital interference under the assumption that the latter exhibits a different symbol rate from the desired signal the proposed equalizer is composed of two stages that are both periodically time varying ptv in order to better match the periodical statistics of the received signal the first stage employs linear ptv filtering to mitigate interference thus allowing the second stage based on the constant modulus algorithm cma to reliably recover the transmitted information symbols computer simulations confirm the effectiveness of the new approach and comparisons with existing blind methods show that a significant performance gain can be attained