On Some Topological and Geometric Properties of Some q-Cesáro Sequence Spaces

Abstract

Mathematical concepts are aesthetic tools that are useful to create methods or solutions to real-world problems in theory and practice, and that sometimes contain symmetrical and asymmetrical structures due to the nature of the problems. In this study, we investigate whether the sequence spaces Xpq, 0≤p<∞, and X∞, which are constructed by q-Cesáro matrix, satisfy some of the further properties described with respect to the bounded linear operators on them. More specifically, we answer to the question: “Which of these spaces have the Approximation, Dunford-Pettis, Radon–Riesz and Hahn–Banach extension properties?”. Furthermore, we try to investigate some geometric properties such as rotundity and smootness of these spaces.