On strong lacunary summability of order ? with respect to modulus functions

Abstract

This research paper focuses on defining the relationships between the sets of strongly lacunary summable and lacunary statistically convergent sequences of complex numbers by using different modulus functions f and g under certain conditions and different orders alpha, beta is an element of (0, 1] such that alpha < beta. Furthermore, for some special modulus functions, we establish the relations between the sets of strongly f-lacunary summable sequences and strongly f-lacunary summable sequences of order alpha.