arXiv subjects
Publications and source records attributed to Necip Simsek.
In general, it is well known the behaviors of the symmetric tri-band matrices on the Hilbert spaces. But the symmetric tri-band matrices have different the behavior on the Banach spaces. The main purpose of this work is to determine the fine spectra of the operator U(s, r, s) defined by symmetric tri-band matrix over the sequence spaces {\ell}_p and bvp.
In this work, we introduce some new generalized sequence space related to the space l(p). Furthermore we investigate some topological properties as the completeness, the isomorphism and also we give some inclusion relations between this sequence space and some of the other sequence spaces. In addition, we compute alpha-, beta- and gamma-duals of this space, and characterize certain matrix transformations on this sequence space.
In this work, we define new sequence spaces by combining generalized weighted mean and difference operator. Afterward, we investigate topological structure which are completeness, AK-property, AD-property. Also, we compute the alpha, beta and gamma duals, and obtain bases for these sequence spaces. Finally, necessary and sufficient conditions on an infinite matrix belonging to the classes (c(u,v,):\ell_{\infty}) and (c(u,v,):c) are established.
In this work, we investigate k-nearly uniform convex(k-NUC) and the uniform Opial properties of the sequence space defined by de la Vallee-Poussin mean. Also we give some corollaries concerning the geometrical properties of this space.
The main purpose of this paper is to introduce a new sequence space by using de la Vallee-Poussin mean and investigate both the modular structure with some geometric properties and some topological properties with respect to the Luxemburg norm.