LACUNARY ALMOST CONVERGENCE AND SOME NEW SEQUENCE SPACES

Abstract

In this paper, we study some new sequence spaces of
strongly lacunary almost summable sequences, which naturally come up for investigation and which will fill up a gap in the existing
literature and introduce the spaces of strongly lacunary almost
summable sequences which happen to be complete paranormed spaces under
certain conditions. Some topological results, characterization of strongly
lacunary almost regular matrices, uniqueness of generalized limits and inclusion
relations of such sequences have been discussed.