New Sequence Spaces and Function Spaces on Interval [0,1]

Abstract EN

We study the sequence spaces and the spaces of functions defined on interval 0,1 in this paper.

By a new summation method of sequences, we find out some new sequence spaces that are interpolating into spaces between ℓp and ℓq and function spaces that are interpolating into the spaces between the polynomial space P0,1 and C∞0,1.

We prove that these spaces of sequences and functions are Banach spaces.