Sequence Spaces and Matrix Transformations
Ekrem Savaș · 2022
P. Schaefer [52] defined σ-conservative, σ-regular, and σ-coercive matrices and obtained the conditions to characterize them. Further, Mursaleen [17] introduced a notion of strong σ-convergence which is a generalization of the idea of strong almost convergence due to Maddox. In [30], Savas defined absolute σ-convergence which naturally emerges from the concept of σ-convergence, furthermore he obtained an inclusion between strongly σ-convergent and absolute σ-convergence. In this chapter, we defined σ-regularity for a series method and determined necessary and sufficient conditions for a series method to be σ-regular and also investigated σ-regularity of dual summability methods and also we introduce some sequence spaces by using invariant mean and sequence of matrices. Later on, we extend those sequence spaces by using a modulus function. Furthermore, some matrix transformations have been examined.