Murat Olgun

Jost Solution and the Spectrum of the Discrete Dirac Systems

We find polynomial-type Jost solution of the self-adjoint discrete Dirac systems. Then we investigate analytical properties and asymptotic behaviour of the Jost solution. Using the Weyl compact perturbation theorem, we prove that discrete Dirac system has the continuous spectrum filling the segment [-2,2]. We also study the eigenvalues of the Dirac system. In particular, we prove that the Dirac system has a finite number of simple real eigenvalues.

Investigation of the spectrum and the Jost solutions of discrete Dirac system on the whole axis

AbstractWe consider the boundary value problem (BVP) for the discrete Dirac equations {yn+1(2)−yn(2)+pnyn(1)=λyn(1),yn−1(1)−yn(1)+qnyn(2)=λyn(2),n∈Z={0,±1,±2,…};y0(1)=0, where (pn) and (qn), n∈Z are real sequences, and λ is an eigenparameter. We find a polynomial type Jost solution of this BVP. Then we investigate the analytical properties and asymptotic behavior of the Jost solution. Using the Weyl compact perturbation theorem, we prove that a self-adjoint discrete Dirac system has a continuous spectrum filling the segment [−2,2]. We also prove that the Dirac system has a finite number of real eigenvalues.

Principal Functions of Nonselfadjoint Discrete Dirac Equations with Spectral Parameter in Boundary Conditions

Let denote the operator generated in by , , , and the boundary condition , where , , , and , are complex sequences, , , and is an eigenparameter. In this paper we investigated the principal functions corresponding to the eigenvalues and the spectral singularities of .

Principal Functions of Non-Selfadjoint Difference Operator with Spectral Parameter in Boundary Conditions

We investigate the principal functions corresponding to the eigenvalues and the spectral singularities of the boundary value problem (BVP) 𝑎𝑛−1𝑦𝑛−1

Fixed points of F-contractive type fuzzy mappings

In this paper, taking into account the recent contractive technique, which was introduced by Wardowski [18], we present a fixed point theorem for F -contractive type fuzzy mappings over a complete metric space.

A Related Fixed Point Theorem for F-Contractions on Two Metric Spaces

Recently, Wardowski in [Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl. 2012] introduced the concept of

Matrix Sturm-Liouville operators with boundary conditions dependent on the spectral parameter

F

Principal Vectors of Matrix-Valued Difference Operators

-contraction on complete metric space which is a proper generalization of Banach contraction principle. In the present paper, we proved a related fixed point theorem with

Non-Selfadjoint Matrix Sturm-Liouville Operators with Eigenvalue-Dependent Boundary Conditions

F

A new aspect to Picard operators with simulation functions

-contraction mappings on two complete metric spaces.