TOPOLOGICAL AND GEOMETRIC PROPERTIES OF SOME NEW SEQUENCE SPACES OF GENERALIZED DIFFERENCE OPERATOR - Braha, Naim l.; Et, Mikail; Karakas, Murat; Mursaleen, Mohammad (Amer Inst Mathematical Sciences-Aims, 2025)
In the present paper, we construct some new Banach spaces by applying the generalized difference operator increment m. We investigate some topological properties of these sequence spaces. Also, we consider it equipped with the Luxemburg norm under which it is a Banach space. Then, we show that it possesses the uniform Opial property and property (H). Finally we give some results about the fixed point theory.
Keywords: Cesaro sequence space; difference operator; k-NUC property; rotundity; Kadec Klee property; uniform Opial property