In recent years, sequential optimality conditions are frequently used for convergence of iterative methods to solve nonlinear constrained optimization problems. The sequential optimality conditions do not require any of the constraint qualications. In this paper, We present the necessary sequential complementary approximate Karush Kuhn Tucker (CAKKT) condition for a point to be a solution of a ...

The spectrum and spectral divisions of band matrices are very new popular topics studies. In this paper, our aims to investigate boundedness Jacobi matrix which is a has important role in physics give subdivisions the spectra, approximate point spectrum, defect compression for special type matrix. Moreover, we will find fine division given by Goldberg with help it.

A Banach space operator T satisfies property(Bgw), a variant property(gw), if the complement in the approximate point spectrum σa(T ) of the semi-B-essential approximate point spectrum σSBF− + (T ) coincides with set of isolated eigenvalues of T of finite multiplicity E(T ). We also introduce properties (Bb), and property (Bgb) in connection with Weyl type theorems, which are analogous, respect...