Journal of Mathematical Sciences

We study the problem of local convergence of the accelerated Newton method for the solution of nonlinear functional equations under generalized Lipschitz conditions for the first- and second-order Fréchet derivatives. We show that the accelerated method is characterized by the quadratic order of convergence and compare it with the classical Newton method.

In this paper, we introduce the notion of a mapping of adjoint G-structures of almost Hermitian manifolds and obtain relations between components of the fundamental tensor fields of an initial almost Hermitian manifold and the conformally transformed manifold. These formulas are applied to the study of the class of Vaisman–Gray manifolds. We prove that in dimension > 4 the class of Vaisman–Gray manifolds coincides with the class of locally conformally nearly K¨ahlerian manifolds.

We establish new properties of the solutions of functional equations with constant delay and linearly transformed argument.

A general scheme which enables us to consider convolution operators with measures acting in a wide class of spaces of distributions on the interval [0, a), 0