the stability problem of the functional equation was conjectured by ulam and was solved by hyers in the case of additive mapping. baker et al. investigated the superstability of the functional equation from a vector space to real numbers.in this paper, we exhibit the superstability of $m$-additive maps on complete non--archimedean spaces via a fixed point method raised by diaz and margolis.

in recent years, some statisticians have studied the signal detection problem by using the random field theory. in this paper we have considered point estimation of the gaussian scale space random field parameters in the bayesian approach. since the posterior distribution for the parameters of interest dose not have a closed form, we introduce the markov chain monte carlo (mcmc) algorithm to ap...

Considering two different metrics on the space of two-dimensional copulas C we prove some Baire category results for important subclasses of copulas, including the families of exchangeable, associative, and Archimedean copulas. From the point of view of Baire categories, with respect to the uniform metric d∞, a typical copula is not symmetric and a typical symmetric copula is not associative, w...

in this paper, we solve the quadratic $alpha$-functional equations $2f(x) + 2f(y) = f(x + y) + alpha^{-2}f(alpha(x-y)); (0.1)$ where $alpha$ is a fixed non-archimedean number with $alpha^{-2}neq 3$. using the fixed point method and the direct method, we prove the hyers-ulam stability of the quadratic $alpha$-functional equation (0.1) in non-archimedean banach spaces.

We estimate Value-at-Risk for sums of dependent random variables. We model multivariate dependent random variables using archimedean copulas. This structure allows one to calculate the asymptotic behaviour of extremal events. An important application of such results are Value-at-Risk estimates for sums of dependent random variables.

we provide fuzzy quasi-metric versions of a fixed point theorem ofgregori and sapena for fuzzy contractive mappings in g-complete fuzzy metricspaces and apply the results to obtain fixed points for contractive mappingsin the domain of words.

We study continuous, nonnegative random variables with a Schur-constant joint survival function. We show that these distributions are characterized by having an Archimedean survival copula, determine the distributions of certain functions of the random variables, and examine dependence properties and correlation coefficients for random variables with Schur-constant survival functions.

in this paper, we introduce a new kind of order, cesaro supermodular order, which includes supermodular order and stochastic order. for this new order, we show that it almost fulfils all desirable properties of a multivariate positive dependence order that have been proposed by joe (1997). also, we obtain some relations between it with other orders. finally, we consider different issues related...