and Applied Analysis 3 x ν αx, t ν x, t/|α| for each α/ 0, xi ν x, t ν y, s ≥ ν x y, t s , xii ν x, · : 0,∞ → 0, 1 is continuous, xiii limt→∞ν x, t 0 and limt→ 0ν x, t 1. In this case μ, ν is called an intuitionistic fuzzy norm. Example 1.4 cf. 37 . Let X, ‖·‖ be a normed space, a∗b ab, and a b min a b, 1 for all a, b ∈ 0, 1 . For all x ∈ X and every t > 0 and k 1, 2, consider μk x, t ⎧ ⎨ ⎩ t t...

We consider Cauchy problem for ordinary differential equation with solution possessing a sequence of multiple poles. propose the generalized reciprocal function method. It reduces calculation pole to retrieval simple zero accordingly chosen function. Advantages this approach are illustrated by numerical examples. two representative test problems which constitute interest verification other meth...

A quantum theoretic representation of real and complex numbers is described here as equivalence classes of Cauchy sequences of quantum states of finite strings of qubits. There are 4 types of qubits each with associated single qubit annihilation creation (a-c) operators that give the state and location of each qubit type on a 2 dimensional integer lattice. The string states, defined as finite p...

In this paper, we study the notion of \(\mathcal{I}\)-localized and \(\mathcal{I}^*\)-localized sequences in \(S\)-metric spaces. Also, investigate some properties related to \(\mathcal{I}\)-Cauchy give idea \(\mathcal{I}\)-barrier a sequence same space. Finally, use for an be when ideal \(\mathcal{I}\) satisfies condition (AP).

The approximate controllability of Sobolev-type Hilfer fractional control differential systems is the main emphasis this paper. We use calculus, Gronwall's inequality, semigroup theory, and Cauchy sequence to examine results for proposed system. application well-known fixed point theorem methodologies avoided in Finally, a heat equation discussed as an example.

n this paper, we apply picard’s iteration method followed by adomian decomposition method to solve a nonlinear singular cauchy problem of euler- poisson- darboux equation. the solution of the problem is much simplified and shorter to arriving at the solution as compared to the technique applied by carroll and showalter (1976)in the solution of singular cauchy problem.

Abstract A refinement of the classic equivalence relation among Cauchy sequences yields a useful infinitesimal-enriched number system. Such an approach can be seen as formalizing Cauchy’s sentiment that null sequence “becomes” infinitesimal. We signal little-noticed construction system with infinitesimals in 1910 publication by Giuseppe Peano, reversing his earlier endorsement Cantor’s belittli...

In [Analysis 1985, 5 (4), 301-313], J.A. Fridy proved an equivalence relation between statistical convergence and Cauchy sequence. this paper, we define $A^{I^{\ast }}$-statistical find under certain conditions, that it is equivalent to $A^{I}$-statistical defined in [Appl. Math. Lett. 2012, 25 733-738]. Moreover, $A^{I}$- sequences some with convergence.

In this paper, we study some basic properties of bicomplex numbers. We introduce two different types partial order relations on numbers, discuss valued metric spaces with respect to orders, and compare them. also define a hyperbolic space, the density natural statistical convergence, Cauchy property sequence numbers investigate in space prove that is complete if only complex are complete.

We consider the Cauchy problem periodic in the spatial variable for the usual cubic nonlinear Schrödinger equation and construct an infinite sequence of invariant measures associated with higher conservation laws for dynamical systems generated by this problem on appropriate phase spaces. In addition, we obtain sufficient conditions for the boundedness of the measures constructed. 2000 Mathemat...