in this paper, we introduce and study fuzzy variational-like inclusion, fuzzy resolvent equation and $h(cdot,cdot)$-$phi$-$eta$-accretive operator in real  uniformly smooth banach spaces. it is established that fuzzy variational-like inclusion is equivalent to a fixed point problem as well as to a fuzzy resolvent equation. this equivalence is used to define an iterative algorithm for solving fu...

in this paper, we state some results on product of operators with closed rangesand we solve the operator equation txs*- sx*t*= a in the general setting of theadjointable operators between hilbert c*-modules, when ts = 1. furthermore, by usingsome block operator matrix techniques, we nd explicit solution of the operator equationtxs*- sx*t*= a.

We consider the flow of Burgers' equation on an open set (small) functions in $L^2([0,1])$. derive explicitly Koopman decomposition flow. identify frequencies and coefficients this as eigenvalues eigenfunctionals operator. prove convergence for $t>0$ small Cauchy data, up to $t=0$ regular data. The $t=0$} leads a `completeness' property basis modes. construct all modes eigenfunctionals, includi...

the aim of this paper is to show that under some mild conditions a functional equation of multiplicative (; )-derivation is superstable on standard operator algebras. furthermore, we prove that this generalized derivation can be a continuous and an inner (; )- derivation.

in the present paper an operator-differential equation of second order in complex domain isconsidered when the coefficients have singularity of pole type at the point z=0. a theorem of existence of thesolution of the equation is proved and the spectral property of the solution is separately investigated when thecoefficients are spectral operators.

In this work‎, ‎an iterative method based on a matrix form of LSQR algorithm is constructed for solving the linear operator equation $mathcal{A}(X)=B$‎ ‎and the minimum Frobenius norm residual problem $||mathcal{A}(X)-B||_F$‎ ‎where $Xin mathcal{S}:={Xin textsf{R}^{ntimes n}~|~X=mathcal{G}(X)}$‎, ‎$mathcal{F}$ is the linear operator from $textsf{R}^{ntimes n}$ onto $textsf{R}^{rtimes s}$‎, ‎$ma...

A quantum theory of a two and three-level laser with injected atomic coherence is developed by using a density operator method, to the best of our knowledge, for the first time. The initial atomic coherence plays an essential role. At steady state, the equation of motion for the density operator yields to exhibit laser without inversion and a phase locking but no threshold for the laser fie...