Abstract. The definition of lacunary strong convergence with respect to a modulus is extended to a definition of lacunary strong A-convergence with respect to a modulus when A = (a ik ) is an infinite matrix of complex numbers. We study some connections between lacunary strong A-convergence with respect to a modulus and lacunary A-statistical convergence.

In this paper we introduce some new difference sequence spaces combining lacunary sequences and Orlicz functions. We establish some inclusion relations between these spaces.

In this paper, we work on the structure of soft linear spaces over a field K and investigate some of its properties. Here, we use the concept of the soft point which was introduced in [2, 6]. We then introduce the soft norm in soft linear spaces. Finally, we examine the properties of this soft normed space and present some investigations about soft continuous operators in the space.

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We introduce the strongly (Vλ,A,p) ‐ summable sequences and give the relation between the spaces of strongly (Vλ,A,p) ‐ summable sequences and strongly (Vλ,A,p) ‐ summable sequences with respect to a modulus function when A = (α ik ) is an infinite matrix of complex numbers and ρ = (pi) is a sequence of positive real numbers. Also we give natural relationship between strongly (Vλ, A,p) ‐ convergence with respect to a modulus function and strongly Sλ (A) ‐ statistical convergence. Key words: De la Vallee‐Poussin mean, modulus function, statistical convergence.