Some New Classes of Sequences and Associated Structures: Difference Sequences, Orlicz Extension, Matrix Class Characterization, Duals and n-Normed Valued Sequences

The theories of difference sequences and associated notions like Orlicz extension, summability, matrix transformation and duality have many uses throughout analysis and applied mathematics. The same is the case for n-normed structures. This book explains various aspects of difference sequence spaces, n-normed valued sequences and demonstrates applications in a coherent manner. This book comprises of 5 chapters starting from Orlicz extension of difference sequences, algebraic and topological properties of difference sequences constructed in comparison with some classical sequence spaces, characterization of matrix classes involving some summable difference sequences spaces, Banach algebra of some matrix classes, computation of equivalent matrix classes, determination of the algebraic duals of some Orlicz extended sets of difference sequences to the construction of n-normed linear space valued sequences with results on convergence and completeness related properties in such classes of sequences. This book will be useful for researchers and professionals in sequence space and associated notions as well as can readily serve as a useful series of lecture notes on the subject.