In this paper is presented a technique for transforming a class of recursive equations called linear equations into iterative equations. Linear equations are characterized by involving at the most one recursive call for any invocation. In contrast to the conventional techniques, the scheme of program transformation presented here involves finding the solution of the given linear equation and tr...

in the present paper, we rst modify the concepts of weakly fuzzy boundedness, strongly fuzzy boundedness, fuzzy continuity, strongly fuzzy continuity and weakly fuzzy continuity. then, we try to nd some relations by making a comparative study of the fuzzy norms of linear operators.

We can write the polynomial solution of the second order linear differential equation of hypergeometric-type φ(x)y + ψ(x)y + λy = 0, where φ and ψ are polynomials, deg φ ≤ 2, degψ = 1 and λ is a constant, among others, by using the Rodrigues operator Rk(φ,u) (see [3]) where u is certain linear operator which satisfies the distributional equation

Given a commuting d-tuple T̄ = (T1, . . . , Td) of otherwise arbitrary operators on a Hilbert space, there is an associated Dirac operator DT̄ . Significant attributes of the d-tuple are best expressed in terms of DT̄ , including the Taylor spectrum and the notion of Fredholmness. In fact, all properties of T̄ derive from its Dirac operator. We introduce a general notion of Dirac operator (in dimen...

If solutions of a non-linear differential equation are contained in solutions of another equation we say that the former equation is a generalized divisor of the latter one. We design an algorithm which finds first-order quasi-linear generalized divisors of a second-order quasi-linear ordinary differential equation. If solutions of an equation contain solutions of a pair of equations we say tha...

In this paper, we state some results on product of operators with closed ranges and we solve the operator equation $TXS^*-SX^*T^*= A$ in the general setting of the adjointable operators between Hilbert $C^*$-modules, when $TS = 1$. Furthermore, by using some block operator matrix techniques, we nd explicit solution of the operator equation $TXS^*-SX^*T^*= A$.

In this paper, a definition of the fundamental operator for the linear autonomous functional differential equation with infinite delay in a Banach space is given, and some sufficient and necessary conditions of the fundamental operator being exponentially stable in abstract phase spaces which satisfy some suitable hypotheses are obtained. Moreover, we discuss the relation between the exponentia...