We approximate the solution u of the Cauchy problem ∂ ∂t u(t, x) r f r. Under natural conditions on solvability in the Sobolev spaces W m p , we show that for any k > 1 one can approximate the solution u with an error of order δ k , by an appropriate combination of the solutions v r along a sequence of time discretization, where δ is proportional to the step size of the grid. This result is obt...

Heuvers, K.J. and D.S. Moak, The solution of the Binet-Cauchy functional equation for square matrices, Discrete Mathematics 88 (1991) 21-32. It is shown that if f : M,(K)+ K is a nonconstant solution of the Binet-Cauchy functional equation for A, B E M,,(K) and if f(E) = 0 where E is the n x n matrix with all entries l/n then f is given by f(A) = m(det A) where m is a multiplicative function on...

In this article we define and investigate statistical analogue of convergence and Cauchy for double sequences in 2-normed space.We also obtain a criteria for a double sequence in 2-normed spaces to be a statistical Cauchy sequence. Mathematics Subject Classification: 40A05; 40A99, 46A70, 46A45

The present study introduces the concepts of ideal convergence (I-convergence), Cauchy (I-Cauchy) sequences, I *-convergence, and *-Cauchy sequences in intuitionistic fuzzy metric spaces. It defines I-limit I-cluster points as a sequence these Afterward, it examines some their basic properties. Lastly, paper discusses whether phenomena should be further investigated.

Intuitionistic set theory without choice axioms does not prove that every Cauchy sequence of rationals has a modulus of convergence, or that the set of Cauchy sequences of rationals is Cauchy complete. Several other related non-provability results are also shown.

In this paper we introduce and investigate I2-convergence, I∗ 2 -convergence, I2-limit points, and I2-cluster points of a double sequence in a fuzzy 2-normed linear space. We prove a decomposition theorem for I2-convergence of double sequences. The notions of I2-double Cauchy and I∗ 2 -double Cauchy sequence are defined, and some of their properties are studied.

In this paper among many other things we prove that the topological left amenability and left amenability of a weighted hypergroup (K, ?) are equivalent. For a normal subgroup H of K, we define a weight function ?? on KIH and obtain connection between left amenability of (K, ?) and (K|H, ??). Let H be a compact subhypergroup of K. We define the weight function on K||H and obtain connection...

We study the stability in the Cauchy Problem for the Helmholtz equation in dependence of the wave number k. For simple geometries, we show analytically that this problem is getting more stable with increasing k. In more detail, there is a subspace of the data space on which the Cauchy Problem is well posed, and this subspace grows with larger k. We call this a subspace of stability. For more ge...

in this paper among many other things we prove that the topological left amenability and left amenability of a weighted hypergroup (k, ?) are equivalent. for a normal subgroup h of k, we define a weight function ?? on kih and obtain connection between left amenability of (k, ?) and (k|h, ??). let h be a compact subhypergroup of k. we define the weight function on k||h and obtain connection betw...

The aim of this paper is to introduce and study the fuzzy neighborhood, the limit fuzzy number, the convergent fuzzy sequence, the bounded fuzzy sequence, and the Cauchy fuzzy sequence on the base which is adopted by Abdul Hameed every real number r is replaced by a fuzzy number r either triangular fuzzy number or singleton fuzzy set fuzzy point . And then, we will consider that some results re...