We consider the question of simultaneous extension of (pseudo)metrics defined on nonempty closed subsets of a compact metrizable space. The main result is a counterpart of the result due to Künzi and Shapiro for the case of extension operators of partial continuous functions and includes, as a special case, Banakh’s theorem on linear regular operators extending (pseudo)metrics.

A Legendre wavelet method is presented for numerical solutions of stochastic Volterra-Fredholm integral equations. The main characteristic of the proposed method is that it reduces stochastic Volterra-Fredholm integral equations into a linear system of equations. Convergence and error analysis of the Legendre wavelets basis are investigated. The efficiency and accuracy of the proposed method wa...

We detail the spectrum of the linearized Vlasov-Poisson equation, and construct an original integro-differential operator which is related to the eigenstructure. It gives a new representation formula for the electric field, and yields new estimates for the linear Landau damping. Then we apply the technique to a problem with a dependence to the Debye length, and show weaker damping for small Deb...

Finite translation planes having a collineation group isomorphic to SL(2, 5)occur in many investigations on minimal normal non-solvable subgroups of linear translation complements. In this paper, we are looking for multiply derived translation planes of the desarguesian plane which have an inherited linear collineation group isomorphic to SL(2, 5). The Hall plane and some of the planes discover...

We consider the vector equation

in this paper, a  fuzzy numerical procedure for solving fuzzy linear volterra integro-differential equations of the second kind under strong  generalized differentiability is designed. unlike the existing numerical methods, we do not replace the original fuzzy equation by a $2times 2$ system ofcrisp equations, that is the main difference between our method  and other numerical methods.error ana...