In this paper, we first introduce a monotone mapping and its resolvent in general metric spaces.Then, we give two new iterative methods  by combining the resolvent method with Halpern's iterative method and viscosity approximation method for  finding a fixed point of monotone mappings and a solution of variational inequalities. We prove convergence theorems of the proposed iterations  in ...

We study the asymptotic behavior of solutions nonlinear fractional evolution equations in Banach spaces. Asymptotically almost periodic on half line are obtained by establishing a sharp estimate resolvent operator family equations. In particular, when semigroup generated A is exponentially stable then conditions existence asymptotically satisfied. An application to partial differential equation...

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...

This paper is concerned with the time-dependent Maxwell’s equations for a plane interface between negative material described by Drude model and vacuum, which fill, respectively, two complementary half-spaces. In first paper, we have constructed generalized Fourier transform diagonalizes Hamiltonian that represents propagation of transverse electric waves. this second use to prove limiting abso...

The convergence analysis of iterative methods for nonlinear eigenvalue problems is in the most cases restricted either to algebraic simple eigenvalues or to polynomial eigenvalue problems. In this paper we consider two classical methods for general holomorphic eigenvalue problems, namely the nonlinear generalized Rayleigh quotient iteration (NGRQI) and the augmented Newton method. For both meth...

This text is a part of an unfinished project which deals with the generalized point interaction (GPI) in one dimension. We employ two natural parametrizations, which are known but have not attracted much attention, to express the resolvent of the GPI Hamiltonian as well as its spectral and scattering properties. It is also shown that the GPI yields one of the simplest models in which a non-triv...

The Riesz basis property of the generalized eigenvector system of a Timoshenko beam with boundary feedback controls applied to two ends is studied in the present paper. The spectral property of the operator A determined by the closed loop system is investigated. It is shown that operator A has compact resolvent and generates a C0 semigroup, and its spectrum consists of two branches and has two ...

The paper offers a self-consistent account of the spectral boundary value problems developed from the perspective of general theory of linear operators in Hilbert spaces. An abstract form of spectral boundary value problem with generalized boundary condition is introduced and results on its solvability complemented by representations of weak and strong solutions are obtained. The question of ex...